Number Systems and Information Systems | BP205T Unit 1

Subject: Computer Applications in Pharmacy

Unit I: Number System & Concept of Information Systems and Software 1. Number System A number system is a method of representing numbers. It defines a set of symbols (digits) and rules for combining them to denote numerical values. The most common feature is the base (radix) , which determines the total number of unique digits used in the system. 1.1. Decimal Number System Also known as Base-10 system . Uses ten unique digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 . It is a positional value system , meaning the value of a digit depends on its position within the number. Each position represents a power of 10. For example, in 123, 3 is 3x10^0, 2 is 2x10^1, 1 is 1x10^2. 1.2. Binary Number System Also known as Base-2 system . Uses two unique digits: 0 and 1 . These digits are called bits (Binary Digits). This is the fundamental number system used by computers as they operate on two states (on/off, high/low voltage). Each position represents a power of 2. 1.3. Octal Number System Also known as Base-8 system . Uses eight unique digits: 0, 1, 2, 3, 4, 5, 6, 7 . It is often used as a compact representation of binary numbers, as three binary digits can represent one octal digit (2^3 = 8). Each position represents a power of 8. 1.4. Hexadecimal Number System Also known as Base-16 system . Uses sixteen unique symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F . Here, A represents 10, B represents 11, and so on, up to F representing 15. Widely used in computer programming (e.g., memory addresses, color codes) due to its ability to represent large binary numbers concisely (four binary digits represent one hexadecimal digit, as 2^4 = 16). Each position represents a power of 16. Comparison of Common Number Systems Number System Base (Radix) Digits Used Examples Decimal 10 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 123 10 , 500 10 Binary 2 0, 1 1011 2 , 100 2 Octal 8 0, 1, 2, 3, 4, 5, 6, 7 77 8 , 123 8 Hexadecimal 16 0-9, A, B, C, D, E, F FF 16 , 1A 16 1.5. Conversions Between Number Systems 1.5.1. Decimal to Binary Conversion To convert a decimal number to binary , repeatedly divide the decimal number by 2 and note down the remainder. The binary equivalent is formed by reading the remainders from bottom to top. For fractional parts, repeatedly multiply by 2 and take the integer part. Worked Example 1: Convert 25 10 to Binary. 25 / 2 = 12 R 1 (LSB) 12 / 2 = 6 R 0 6 / 2 = 3 R 0 3 / 2 = 1 R 1 1 / 2 = 0 R 1 (MSB) Reading the remainders from bottom to top, 25 10 = 11001 2 . Topper Secrets: Remember the "Divide by 2, Read Up" rule for integer part conversions. For fractional parts, it's "Multiply by 2, Read Down" (integer parts only). 1.5.2. Binary to Decimal Conversion To convert a binary number to decimal , multiply each bit by its positional weight (power of 2) and sum the results. The positional weight starts from 2 0 for the rightmost bit, increasing by one for each position to the left. For fractional parts, powers become negative (2 -1 , 2 -2 , etc.). Worked Example 2: Convert 11011 2 to Decimal. 1 1 0 1 1 2^4 2^3 2^2 2^1 2^0 16 8 4 2 1 (1 * 2^4) + (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0) = (1 * 16) + (1 * 8) + (0 * 4) + (1 * 2) + (1 * 1) = 16 + 8 + 0 + 2 + 1 = 27 So, 11011 2 = 27 10 . 1.5.3. Octal to Binary Conversion To convert an octal number to binary , convert each octal digit into its 3-bit binary equivalent. Since 2 3 = 8, each octal digit can be uniquely represented by three binary bits. Worked Example 3: Convert 634 8 to Binary. Octal Digit: 6 3 4 Binary Equivalent: 6 -> 110 3 -> 011 4 -> 100 Combine the binary equivalents: 110011100 So, 634 8 = 110011100 2 . Common Exam Question: Be prepared to convert between any two given number systems, especially Decimal to Binary and vice-versa, as well as Octal/Hexadecimal to Binary and vice-versa (even though Octal to Binary is explicitly mentioned, Binary to Octal is its natural inverse). 1.6. Binary Arithmetic 1.6.1. Binary Addition Binary addition follows the same principles as decimal addition, but with only two digits (0 and 1). Binary Addition Rules Operation Sum Carry 0 + 0 0 0 0 + 1 1 0 1 + 0 1 0 1 + 1 0 1 1 + 1 + 1 1 1 Worked Example 4: Add 1011 2 and 1101 2 . 1 0 1 1 (11 in decimal) + 1 1 0 1 (13 in decimal) ---------- 1 1 0 0 0 (24 in decimal) Explanation: (Carries) 1 1 1 0 1 0 1 1 + 1 1 0 1 --------- 1 1 0 0 0 1.6.2. Binary Subtraction Binary subtraction can be performed directly or using complements, which is often preferred in digital circuits for simplification. 1.6.2.1. One's Complement Method The one's complement of a binary number is obtained by inverting all its bits (changing 0s to 1s and 1s to 0s). To subtract B from A using one's complement: Find the one's complement of B

Home NotesComputer Applications in Pharmacy

Computer Applications in Pharmacy Hub

Number Systems and Information Systems | BP205T Unit 1

PCI Verified By Arvind Sharma, B.Pharm, M.Pharm, Assistant Professor, MUIT Recent 15 min read Computer Applications in Pharmacy

Unit I: Number System & Concept of Information Systems and Software

1. Number System

A number system is a method of representing numbers. It defines a set of symbols (digits) and rules for combining them to denote numerical values. The most common feature is the base (radix), which determines the total number of unique digits used in the system.

1.1. Decimal Number System

Also known as Base-10 system.
Uses ten unique digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
It is a positional value system, meaning the value of a digit depends on its position within the number.
Each position represents a power of 10. For example, in 123, 3 is 3x10^0, 2 is 2x10^1, 1 is 1x10^2.

1.2. Binary Number System

Also known as Base-2 system.
Uses two unique digits: 0 and 1. These digits are called bits (Binary Digits).
This is the fundamental number system used by computers as they operate on two states (on/off, high/low voltage).
Each position represents a power of 2.

1.3. Octal Number System

Also known as Base-8 system.
Uses eight unique digits: 0, 1, 2, 3, 4, 5, 6, 7.
It is often used as a compact representation of binary numbers, as three binary digits can represent one octal digit (2^3 = 8).
Each position represents a power of 8.

1.4. Hexadecimal Number System

Also known as Base-16 system.
Uses sixteen unique symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.
Here, A represents 10, B represents 11, and so on, up to F representing 15.
Widely used in computer programming (e.g., memory addresses, color codes) due to its ability to represent large binary numbers concisely (four binary digits represent one hexadecimal digit, as 2^4 = 16).
Each position represents a power of 16.

Comparison of Common Number Systems
Number System	Base (Radix)	Digits Used	Examples
Decimal	10	0, 1, 2, 3, 4, 5, 6, 7, 8, 9	123₁₀, 500₁₀
Binary	2	0, 1	1011₂, 100₂
Octal	8	0, 1, 2, 3, 4, 5, 6, 7	77₈, 123₈
Hexadecimal	16	0-9, A, B, C, D, E, F	FF₁₆, 1A₁₆

1.5. Conversions Between Number Systems

1.5.1. Decimal to Binary Conversion

To convert a decimal number to binary, repeatedly divide the decimal number by 2 and note down the remainder. The binary equivalent is formed by reading the remainders from bottom to top. For fractional parts, repeatedly multiply by 2 and take the integer part.

Worked Example 1: Convert 25₁₀ to Binary.

25 / 2 = 12 R 1 (LSB)
12 / 2 = 6  R 0
6  / 2 = 3  R 0
3  / 2 = 1  R 1
1  / 2 = 0  R 1 (MSB)

Reading the remainders from bottom to top, 25₁₀ = 11001₂.

Topper Secrets: Remember the "Divide by 2, Read Up" rule for integer part conversions. For fractional parts, it's "Multiply by 2, Read Down" (integer parts only).

1.5.2. Binary to Decimal Conversion

To convert a binary number to decimal, multiply each bit by its positional weight (power of 2) and sum the results. The positional weight starts from 2⁰ for the rightmost bit, increasing by one for each position to the left. For fractional parts, powers become negative (2^-1, 2^-2, etc.).

Worked Example 2: Convert 11011₂ to Decimal.

1   1   0   1   1
2^4 2^3 2^2 2^1 2^0
16  8   4   2   1

(1 * 2^4) + (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0)
= (1 * 16) + (1 * 8) + (0 * 4) + (1 * 2) + (1 * 1)
= 16 + 8 + 0 + 2 + 1
= 27

So, 11011₂ = 27₁₀.

1.5.3. Octal to Binary Conversion

To convert an octal number to binary, convert each octal digit into its 3-bit binary equivalent. Since 2³ = 8, each octal digit can be uniquely represented by three binary bits.

Worked Example 3: Convert 634₈ to Binary.

Octal Digit:  6   3   4
Binary Equivalent:
6 -> 110
3 -> 011
4 -> 100

Combine the binary equivalents: 110011100

So, 634₈ = 110011100₂.

Common Exam Question: Be prepared to convert between any two given number systems, especially Decimal to Binary and vice-versa, as well as Octal/Hexadecimal to Binary and vice-versa (even though Octal to Binary is explicitly mentioned, Binary to Octal is its natural inverse).

1.6. Binary Arithmetic

1.6.1. Binary Addition

Binary addition follows the same principles as decimal addition, but with only two digits (0 and 1).

Binary Addition Rules
Operation	Sum	Carry
0 + 0	0	0
0 + 1	1	0
1 + 0	1	0
1 + 1	0	1
1 + 1 + 1	1	1

Worked Example 4: Add 1011₂ and 1101₂.

  1 0 1 1   (11 in decimal)
+ 1 1 0 1   (13 in decimal)
----------
1 1 0 0 0   (24 in decimal)

Explanation:
  (Carries) 1 1 1 0
          1 0 1 1
        + 1 1 0 1
        ---------
        1 1 0 0 0

1.6.2. Binary Subtraction

Binary subtraction can be performed directly or using complements, which is often preferred in digital circuits for simplification.

1.6.2.1. One's Complement Method

The one's complement of a binary number is obtained by inverting all its bits (changing 0s to 1s and 1s to 0s). To subtract B from A using one's complement:

Find the one's complement of B.
Add A to the one's complement of B.
If there is a carry-out (end-around carry), add it to the result (LSB). The result is positive.
If there is no carry-out, the result is negative, and it's the one's complement of the sum.

Worked Example 5: Subtract 0101₂ from 1011₂ (11 - 5).

Minuend (A) = 1011₂
Subtrahend (B) = 0101₂
One's complement of B (0101) = 1010

Add A and one's complement of B:

There is a carry-out (1). Add this carry-out to the LSB of the result:

          0101
        +    1  (End-around carry)
        -------
          0110

So, 1011₂ - 0101₂ = 0110₂ (which is 6 in decimal).

Worked Example 6: Subtract 1011₂ from 0101₂ (5 - 11).

Minuend (A) = 0101₂
Subtrahend (B) = 1011₂
One's complement of B (1011) = 0100

Add A and one's complement of B:

There is no carry-out. The result is negative. Take the one's complement of 1001, which is 0110.

So, 0101₂ - 1011₂ = -0110₂ (which is -6 in decimal).

1.6.2.2. Two's Complement Method

The two's complement of a binary number is obtained by adding 1 to its one's complement. To subtract B from A using two's complement:

Find the two's complement of B.
Add A to the two's complement of B.
If there is a carry-out, discard it. The remaining result is positive.
If there is no carry-out, the result is negative, and it's in two's complement form. To get the magnitude, take the two's complement of the result.

Worked Example 7: Subtract 0101₂ from 1011₂ (11 - 5).

Minuend (A) = 1011₂
Subtrahend (B) = 0101₂
One's complement of B (0101) = 1010
Two's complement of B = 1010 + 1 = 1011

Add A and two's complement of B:

Discard the carry-out (1). The result is 0110₂.

So, 1011₂ - 0101₂ = 0110₂ (which is 6 in decimal).

Worked Example 8: Subtract 1011₂ from 0101₂ (5 - 11).

Minuend (A) = 0101₂
Subtrahend (B) = 1011₂
One's complement of B (1011) = 0100
Two's complement of B = 0100 + 1 = 0101

Add A and two's complement of B:

There is no carry-out. The result 1010₂ is negative and in two's complement form. To get the magnitude, take the two's complement of 1010:
- One's complement of 1010 = 0101
- Two's complement of 1010 = 0101 + 1 = 0110

So, 0101₂ - 1011₂ = -0110₂ (which is -6 in decimal).

Topper Secrets: Two's complement subtraction is more commonly used in computers because it simplifies hardware design by treating subtraction as addition, eliminating the need for end-around carry logic.

1.6.3. Binary Multiplication

Binary multiplication is similar to decimal multiplication. It involves multiplying the multiplicand by each bit of the multiplier, shifting the partial products, and then summing them.

Binary Multiplication Rules
Operation	Product
0 x 0	0
0 x 1	0
1 x 0	0
1 x 1	1

Worked Example 9: Multiply 101₂ by 11₂ (5 * 3).

    101   (multiplicand)
  x 011   (multiplier)
  -----
    101   (101 * 1)
+ 1010   (101 * 1, shifted left by one position)
-------
  1111   (Result)

So, 101₂ * 11₂ = 1111₂ (which is 15 in decimal).

1.6.4. Binary Division

Binary division is performed using a process similar to long division in decimal. It involves repeated subtraction of the divisor from the dividend.

Worked Example 10: Divide 1100₂ by 10₂ (12 / 2).

        110   (Quotient)
      _______
10   ) 1100
       - 10
       ----
         010
       -  10
       ----
          000
        -  00
        ----
           00

So, 1100₂ / 10₂ = 110₂ (which is 6 in decimal).

2. Concept of Information Systems and Software

2.1. Concept of Information Systems (IS)

An Information System (IS) is a set of interrelated components working together to collect, process, store, and disseminate information to support decision-making, coordination, control, analysis, and visualization in an organization.

Components of IS: Hardware, Software, Data, People, and Processes.
Role in Pharmacy: Essential for managing patient records, drug inventories, billing, research data, and clinical decision support.

2.2. Concept of Software

Software refers to a set of instructions, data, or programs used to operate computers and execute specific tasks. It is a general term used to describe computer programs, scripts, and applications that run on a device.

System Software: Manages and controls computer hardware and provides a platform for other software to run. Examples: Operating systems (Windows, Linux), device drivers.
Application Software: Performs specific tasks for end-users. Examples: Word processors (MS Word), spreadsheets (MS Excel), pharmacy management systems, web browsers.

2.3. Information Gathering

Information gathering, also known as data collection or fact-finding, is the initial stage in the software development process where analysts collect detailed information about the existing system and the requirements for the new system from various stakeholders.

Methods of Information Gathering:
- Interviews: Direct conversation with stakeholders to elicit detailed requirements.
- Questionnaires/Surveys: Efficient for gathering information from a large number of people.
- Observation: Watching users perform tasks to understand processes and identify pain points.
- Document Analysis: Reviewing existing system documentation, reports, forms, and procedures to understand current operations.
- Prototyping: Developing a preliminary version of the system to get user feedback.

2.4. Requirement and Feasibility Analysis

This phase defines what the new system should do and determines if it is practical and achievable.

2.4.1. Requirement Analysis

Requirement analysis is the process of defining the needs and expectations of the users for a new or modified product. It focuses on identifying, understanding, and documenting the features and functionalities that the system must possess.

Types of Requirements:
- Functional Requirements: Describe what the system MUST do (e.g., "The system shall allow pharmacists to update drug inventory").
- Non-functional Requirements: Describe how the system SHOULD perform (e.g., "The system shall respond to user queries within 2 seconds," "The system shall be secure against unauthorized access"). This includes performance, security, usability, reliability, scalability.

2.4.2. Feasibility Analysis

A feasibility study evaluates the practicality of a proposed project, ensuring it is technically possible, financially viable, and operationally desirable. It helps in making a "go/no-go" decision.

Types of Feasibility:
- Technical Feasibility: Can the project be built with existing technology? Is the required hardware/software available?
- Economic Feasibility: Is the project financially viable? Will the benefits outweigh the costs (Cost-Benefit Analysis)?
- Operational Feasibility: Will the system work in the existing organizational structure? Is it compatible with the existing work environment and user skills?
- Schedule Feasibility: Can the project be completed within the given time frame?
- Legal and Ethical Feasibility: Does the project comply with all laws, regulations (e.g., HIPAA for patient data), and ethical considerations?

2.5. Data Flow Diagrams (DFD)

A Data Flow Diagram (DFD) is a graphical representation of the "flow" of data through an information system. It illustrates how data is processed and stored within a system, without detailing hardware or software specifications.

Purpose: To visualize the boundaries of the system, the data it consumes and produces, and the places where data is stored and changed.

DFD Components (Yourdon-DeMarco Notation):

DFD Symbols and Description
Symbol	Name	Description
	External Entity (Terminator)	Represents sources or destinations of data outside the system (e.g., Patient, Supplier, Pharmacy Staff).
	Process	Transforms incoming data flow(s) into outgoing data flow(s) (e.g., Dispense Medication, Process Prescription).
	Data Store	A place where data is held for later use (e.g., Patient Records, Drug Inventory).
	Data Flow	The movement of data from one component to another, represented by an arrow with a label describing the data.

Levels of DFD:
- Context Diagram (Level 0 DFD): The highest-level DFD, representing the entire system as a single process with all its external entities and major data flows. It shows the system's boundary.
- Level 1 DFD: Decomposes the single process from the context diagram into its major sub-processes, showing how data flows between them and to/from data stores and external entities.

Common University Exam Question: Draw a DFD for a simple scenario like "Prescription Dispensing System" or "Student Enrollment System." Ensure to correctly use all four symbols.

2.6. Process Specifications

Process specifications (also known as mini-specs) describe the detailed logic of a DFD process. They are used when the logic of a process cannot be adequately described in the DFD itself.

Purpose: To precisely define what a process does, including conditions, calculations, and decision rules.
Methods for documenting process specifications: Structured English, Decision Tables, Decision Trees.

2.7. Input/Output Design

This phase focuses on how data enters the system (input) and how information is presented to the user (output).

2.7.1. Input Design

Input design involves designing the user interface and data entry forms or screens to capture accurate and efficient data from the user or other systems.

Goals: Minimize data entry errors, simplify data entry, ensure consistency, and reduce processing time.
Considerations: Data validation, input masks, default values, clear labels, appropriate input controls (text boxes, dropdowns, checkboxes).

2.7.2. Output Design

Output design focuses on generating meaningful, useful, and attractive information for end-users, typically in the form of reports, screen displays, or digital documents.

Goals: Present information clearly and concisely, meet user needs, ensure accuracy, and be timely.
Types of Output: Printed reports (e.g., patient billing, drug inventory reports), screen displays, audio, email, SMS alerts.

2.8. Process Life Cycle (Software Development Life Cycle - SDLC)

The Software Development Life Cycle (SDLC) is a framework defining tasks performed at each step in the software development process. It is a systematic approach to designing, developing, testing, and deploying high-quality software.

Common Phases of SDLC:

Planning: Defines the scope, objectives, and feasibility of the project. Involves requirement gathering and initial analysis.
Analysis: Detailed study of the system's requirements, creating models like DFDs, and documenting functional and non-functional requirements.
Design: Translating requirements into a detailed system design, including architecture, user interface, database structure, and module specifications.
Implementation/Development: Coding the software based on the design specifications.
Testing: Systematically checking for errors and defects to ensure the software meets requirements and works correctly.
Deployment/Implementation: Releasing the software to the users for operation. This may involve installation, configuration, and training.
Maintenance: Ongoing support, updates, bug fixes, and enhancements to keep the system running effectively and adapt to changing needs.

Simplified SDLC Flow:

Planning -> Analysis -> Design -> Implementation -> Testing -> Deployment -> Maintenance

Topper Secrets: Understand that SDLC is not always strictly sequential (waterfall model). Other models like Agile, Spiral, and V-model exist, which might introduce iterations or concurrent phases, but the core activities remain similar.

2.9. Planning and Managing the Project

Project management is the application of knowledge, skills, tools, and techniques to project activities to meet the project requirements. In software development, it ensures that software projects are delivered on time, within budget, and to specification.

Key Aspects of Project Management:
- Scope Management: Defining and controlling what is and is not included in the project.
- Time Management: Estimating, scheduling, and controlling project activities to ensure timely completion.
- Cost Management: Planning, estimating, budgeting, financing, funding, managing, and controlling costs so that the project can be completed within the approved budget.
- Quality Management: Ensuring the project and its deliverables meet specified quality standards.
- Risk Management: Identifying, assessing, and responding to project risks.
- Resource Management: Acquiring, managing, and utilizing team members and other resources effectively.
- Communication Management: Planning, managing, and distributing information effectively.
- Stakeholder Management: Identifying all people or organizations impacted by the project and managing their expectations and engagement.
Phases of Project Management:
1. Initiation: Defining a new project or a new phase of an existing project.
2. Planning: Establishing the scope, refining objectives, and defining the course of action required to attain the objectives.
3. Execution: Carrying out the project plan.
4. Monitoring & Control: Tracking, reviewing, and regulating the progress and performance of the project; identifying any areas in which changes to the plan are required; and initiating the corresponding changes.
5. Closure: Finalizing all activities across all process groups to formally close the project or phase.

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Computer Applications in Pharmacy Hub

Number Systems and Information Systems | BP205T Unit 1

PCI Verified By Arvind Sharma, B.Pharm, M.Pharm, Assistant Professor, MUIT Recent 15 min read Computer Applications in Pharmacy

Unit I: Number System & Concept of Information Systems and Software

1. Number System

1.1. Decimal Number System

Also known as Base-10 system.
Uses ten unique digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
It is a positional value system, meaning the value of a digit depends on its position within the number.
Each position represents a power of 10. For example, in 123, 3 is 3x10^0, 2 is 2x10^1, 1 is 1x10^2.

1.2. Binary Number System

Also known as Base-2 system.
Uses two unique digits: 0 and 1. These digits are called bits (Binary Digits).
This is the fundamental number system used by computers as they operate on two states (on/off, high/low voltage).
Each position represents a power of 2.

1.3. Octal Number System

Also known as Base-8 system.
Uses eight unique digits: 0, 1, 2, 3, 4, 5, 6, 7.
It is often used as a compact representation of binary numbers, as three binary digits can represent one octal digit (2^3 = 8).
Each position represents a power of 8.

1.4. Hexadecimal Number System

Also known as Base-16 system.
Uses sixteen unique symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.
Here, A represents 10, B represents 11, and so on, up to F representing 15.
Widely used in computer programming (e.g., memory addresses, color codes) due to its ability to represent large binary numbers concisely (four binary digits represent one hexadecimal digit, as 2^4 = 16).
Each position represents a power of 16.

Comparison of Common Number Systems
Number System	Base (Radix)	Digits Used	Examples
Decimal	10	0, 1, 2, 3, 4, 5, 6, 7, 8, 9	123₁₀, 500₁₀
Binary	2	0, 1	1011₂, 100₂
Octal	8	0, 1, 2, 3, 4, 5, 6, 7	77₈, 123₈
Hexadecimal	16	0-9, A, B, C, D, E, F	FF₁₆, 1A₁₆

1.5. Conversions Between Number Systems

1.5.1. Decimal to Binary Conversion

Worked Example 1: Convert 25₁₀ to Binary.

25 / 2 = 12 R 1 (LSB)
12 / 2 = 6  R 0
6  / 2 = 3  R 0
3  / 2 = 1  R 1
1  / 2 = 0  R 1 (MSB)

Reading the remainders from bottom to top, 25₁₀ = 11001₂.

Topper Secrets: Remember the "Divide by 2, Read Up" rule for integer part conversions. For fractional parts, it's "Multiply by 2, Read Down" (integer parts only).

1.5.2. Binary to Decimal Conversion

Worked Example 2: Convert 11011₂ to Decimal.

1   1   0   1   1
2^4 2^3 2^2 2^1 2^0
16  8   4   2   1

(1 * 2^4) + (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0)
= (1 * 16) + (1 * 8) + (0 * 4) + (1 * 2) + (1 * 1)
= 16 + 8 + 0 + 2 + 1
= 27

So, 11011₂ = 27₁₀.

1.5.3. Octal to Binary Conversion

To convert an octal number to binary, convert each octal digit into its 3-bit binary equivalent. Since 2³ = 8, each octal digit can be uniquely represented by three binary bits.

Worked Example 3: Convert 634₈ to Binary.

Octal Digit:  6   3   4
Binary Equivalent:
6 -> 110
3 -> 011
4 -> 100

Combine the binary equivalents: 110011100

So, 634₈ = 110011100₂.

1.6. Binary Arithmetic

1.6.1. Binary Addition

Binary addition follows the same principles as decimal addition, but with only two digits (0 and 1).

Binary Addition Rules
Operation	Sum	Carry
0 + 0	0	0
0 + 1	1	0
1 + 0	1	0
1 + 1	0	1
1 + 1 + 1	1	1

Worked Example 4: Add 1011₂ and 1101₂.

  1 0 1 1   (11 in decimal)
+ 1 1 0 1   (13 in decimal)
----------
1 1 0 0 0   (24 in decimal)

Explanation:
  (Carries) 1 1 1 0
          1 0 1 1
        + 1 1 0 1
        ---------
        1 1 0 0 0

1.6.2. Binary Subtraction

Binary subtraction can be performed directly or using complements, which is often preferred in digital circuits for simplification.

1.6.2.1. One's Complement Method

The one's complement of a binary number is obtained by inverting all its bits (changing 0s to 1s and 1s to 0s). To subtract B from A using one's complement:

Find the one's complement of B.
Add A to the one's complement of B.
If there is a carry-out (end-around carry), add it to the result (LSB). The result is positive.
If there is no carry-out, the result is negative, and it's the one's complement of the sum.

Worked Example 5: Subtract 0101₂ from 1011₂ (11 - 5).

Minuend (A) = 1011₂
Subtrahend (B) = 0101₂
One's complement of B (0101) = 1010

Add A and one's complement of B:

There is a carry-out (1). Add this carry-out to the LSB of the result:

          0101
        +    1  (End-around carry)
        -------
          0110

So, 1011₂ - 0101₂ = 0110₂ (which is 6 in decimal).

Worked Example 6: Subtract 1011₂ from 0101₂ (5 - 11).

Minuend (A) = 0101₂
Subtrahend (B) = 1011₂
One's complement of B (1011) = 0100

Add A and one's complement of B:

There is no carry-out. The result is negative. Take the one's complement of 1001, which is 0110.

So, 0101₂ - 1011₂ = -0110₂ (which is -6 in decimal).

1.6.2.2. Two's Complement Method

The two's complement of a binary number is obtained by adding 1 to its one's complement. To subtract B from A using two's complement:

Find the two's complement of B.
Add A to the two's complement of B.
If there is a carry-out, discard it. The remaining result is positive.
If there is no carry-out, the result is negative, and it's in two's complement form. To get the magnitude, take the two's complement of the result.

Worked Example 7: Subtract 0101₂ from 1011₂ (11 - 5).

Minuend (A) = 1011₂
Subtrahend (B) = 0101₂
One's complement of B (0101) = 1010
Two's complement of B = 1010 + 1 = 1011

Add A and two's complement of B:

Discard the carry-out (1). The result is 0110₂.

So, 1011₂ - 0101₂ = 0110₂ (which is 6 in decimal).

Worked Example 8: Subtract 1011₂ from 0101₂ (5 - 11).

Minuend (A) = 0101₂
Subtrahend (B) = 1011₂
One's complement of B (1011) = 0100
Two's complement of B = 0100 + 1 = 0101

Add A and two's complement of B:

There is no carry-out. The result 1010₂ is negative and in two's complement form. To get the magnitude, take the two's complement of 1010:
- One's complement of 1010 = 0101
- Two's complement of 1010 = 0101 + 1 = 0110

So, 0101₂ - 1011₂ = -0110₂ (which is -6 in decimal).

1.6.3. Binary Multiplication

Binary multiplication is similar to decimal multiplication. It involves multiplying the multiplicand by each bit of the multiplier, shifting the partial products, and then summing them.

Binary Multiplication Rules
Operation	Product
0 x 0	0
0 x 1	0
1 x 0	0
1 x 1	1

Worked Example 9: Multiply 101₂ by 11₂ (5 * 3).

    101   (multiplicand)
  x 011   (multiplier)
  -----
    101   (101 * 1)
+ 1010   (101 * 1, shifted left by one position)
-------
  1111   (Result)

So, 101₂ * 11₂ = 1111₂ (which is 15 in decimal).

1.6.4. Binary Division

Binary division is performed using a process similar to long division in decimal. It involves repeated subtraction of the divisor from the dividend.

Worked Example 10: Divide 1100₂ by 10₂ (12 / 2).

        110   (Quotient)
      _______
10   ) 1100
       - 10
       ----
         010
       -  10
       ----
          000
        -  00
        ----
           00

So, 1100₂ / 10₂ = 110₂ (which is 6 in decimal).

2. Concept of Information Systems and Software

2.1. Concept of Information Systems (IS)

Components of IS: Hardware, Software, Data, People, and Processes.
Role in Pharmacy: Essential for managing patient records, drug inventories, billing, research data, and clinical decision support.

2.2. Concept of Software

System Software: Manages and controls computer hardware and provides a platform for other software to run. Examples: Operating systems (Windows, Linux), device drivers.
Application Software: Performs specific tasks for end-users. Examples: Word processors (MS Word), spreadsheets (MS Excel), pharmacy management systems, web browsers.

2.3. Information Gathering

Methods of Information Gathering:
- Interviews: Direct conversation with stakeholders to elicit detailed requirements.
- Questionnaires/Surveys: Efficient for gathering information from a large number of people.
- Observation: Watching users perform tasks to understand processes and identify pain points.
- Document Analysis: Reviewing existing system documentation, reports, forms, and procedures to understand current operations.
- Prototyping: Developing a preliminary version of the system to get user feedback.

2.4. Requirement and Feasibility Analysis

This phase defines what the new system should do and determines if it is practical and achievable.

2.4.1. Requirement Analysis

Types of Requirements:
- Functional Requirements: Describe what the system MUST do (e.g., "The system shall allow pharmacists to update drug inventory").
- Non-functional Requirements: Describe how the system SHOULD perform (e.g., "The system shall respond to user queries within 2 seconds," "The system shall be secure against unauthorized access"). This includes performance, security, usability, reliability, scalability.

2.4.2. Feasibility Analysis

A feasibility study evaluates the practicality of a proposed project, ensuring it is technically possible, financially viable, and operationally desirable. It helps in making a "go/no-go" decision.

Types of Feasibility:
- Technical Feasibility: Can the project be built with existing technology? Is the required hardware/software available?
- Economic Feasibility: Is the project financially viable? Will the benefits outweigh the costs (Cost-Benefit Analysis)?
- Operational Feasibility: Will the system work in the existing organizational structure? Is it compatible with the existing work environment and user skills?
- Schedule Feasibility: Can the project be completed within the given time frame?
- Legal and Ethical Feasibility: Does the project comply with all laws, regulations (e.g., HIPAA for patient data), and ethical considerations?

2.5. Data Flow Diagrams (DFD)

Purpose: To visualize the boundaries of the system, the data it consumes and produces, and the places where data is stored and changed.

DFD Components (Yourdon-DeMarco Notation):

DFD Symbols and Description
Symbol	Name	Description
	External Entity (Terminator)	Represents sources or destinations of data outside the system (e.g., Patient, Supplier, Pharmacy Staff).
	Process	Transforms incoming data flow(s) into outgoing data flow(s) (e.g., Dispense Medication, Process Prescription).
	Data Store	A place where data is held for later use (e.g., Patient Records, Drug Inventory).
	Data Flow	The movement of data from one component to another, represented by an arrow with a label describing the data.

Levels of DFD:
- Context Diagram (Level 0 DFD): The highest-level DFD, representing the entire system as a single process with all its external entities and major data flows. It shows the system's boundary.
- Level 1 DFD: Decomposes the single process from the context diagram into its major sub-processes, showing how data flows between them and to/from data stores and external entities.

Common University Exam Question: Draw a DFD for a simple scenario like "Prescription Dispensing System" or "Student Enrollment System." Ensure to correctly use all four symbols.

2.6. Process Specifications

Process specifications (also known as mini-specs) describe the detailed logic of a DFD process. They are used when the logic of a process cannot be adequately described in the DFD itself.

Purpose: To precisely define what a process does, including conditions, calculations, and decision rules.
Methods for documenting process specifications: Structured English, Decision Tables, Decision Trees.

2.7. Input/Output Design

This phase focuses on how data enters the system (input) and how information is presented to the user (output).

2.7.1. Input Design

Input design involves designing the user interface and data entry forms or screens to capture accurate and efficient data from the user or other systems.

Goals: Minimize data entry errors, simplify data entry, ensure consistency, and reduce processing time.
Considerations: Data validation, input masks, default values, clear labels, appropriate input controls (text boxes, dropdowns, checkboxes).

2.7.2. Output Design

Output design focuses on generating meaningful, useful, and attractive information for end-users, typically in the form of reports, screen displays, or digital documents.

Goals: Present information clearly and concisely, meet user needs, ensure accuracy, and be timely.
Types of Output: Printed reports (e.g., patient billing, drug inventory reports), screen displays, audio, email, SMS alerts.

2.8. Process Life Cycle (Software Development Life Cycle - SDLC)

Common Phases of SDLC:

Planning: Defines the scope, objectives, and feasibility of the project. Involves requirement gathering and initial analysis.
Analysis: Detailed study of the system's requirements, creating models like DFDs, and documenting functional and non-functional requirements.
Design: Translating requirements into a detailed system design, including architecture, user interface, database structure, and module specifications.
Implementation/Development: Coding the software based on the design specifications.
Testing: Systematically checking for errors and defects to ensure the software meets requirements and works correctly.
Deployment/Implementation: Releasing the software to the users for operation. This may involve installation, configuration, and training.
Maintenance: Ongoing support, updates, bug fixes, and enhancements to keep the system running effectively and adapt to changing needs.

Simplified SDLC Flow:

Planning -> Analysis -> Design -> Implementation -> Testing -> Deployment -> Maintenance

2.9. Planning and Managing the Project

Key Aspects of Project Management:
- Scope Management: Defining and controlling what is and is not included in the project.
- Time Management: Estimating, scheduling, and controlling project activities to ensure timely completion.
- Cost Management: Planning, estimating, budgeting, financing, funding, managing, and controlling costs so that the project can be completed within the approved budget.
- Quality Management: Ensuring the project and its deliverables meet specified quality standards.
- Risk Management: Identifying, assessing, and responding to project risks.
- Resource Management: Acquiring, managing, and utilizing team members and other resources effectively.
- Communication Management: Planning, managing, and distributing information effectively.
- Stakeholder Management: Identifying all people or organizations impacted by the project and managing their expectations and engagement.
Phases of Project Management:
1. Initiation: Defining a new project or a new phase of an existing project.
2. Planning: Establishing the scope, refining objectives, and defining the course of action required to attain the objectives.
3. Execution: Carrying out the project plan.
4. Monitoring & Control: Tracking, reviewing, and regulating the progress and performance of the project; identifying any areas in which changes to the plan are required; and initiating the corresponding changes.
5. Closure: Finalizing all activities across all process groups to formally close the project or phase.

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