Looking for comprehensive PGDCA (Post Graduate Diploma in Computer Applications) notes on Number Systems for the 2026–27 academic session? Access complete theory explanations, solved base conversion steps, binary arithmetic, 1’s and 2’s complement, objective MCQs, and exam-oriented solutions covering Binary, Octal, Decimal, and Hexadecimal number systems tailored for university diploma exams.
Number System
Computers utilize mathematical positional number systems to process and represent all digital information.
Core Computer Number Systems:
- Binary System (Base 2):Uses digits 0, 1. Universal language of digital electronic circuits.
- Octal System (Base 8): Uses digits 0, 1, 2, 3, 4, 5, 6, 7.
- Decimal System (Base 10): Standard human number system using digits 0 to 9.
- Hexadecimal System (Base 16): Uses digits 0 to 9 and letters A to F (where A=10, B=11, …, F=15). Used for memory addresses and color codes.
Quick Base Summary Table:
| Number System | Base / Radix | Digits / Symbols Used | Example |
| Binary | 2 | 0, 1 | (101101)2 |
| Octal | 8 | 0, 1, 2, 3, 4, 5, 6, 7 | (67)8 |
| Decimal | 10 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 | (55)10 |
| Hexadecimal | 16 | 0 to 9, A to F | (3B)16 |
PGDCA Number System Notes
Q1. Identify the base (radix) and available symbols for Binary and Hexadecimal number systems. [2 Marks]
Answer:
Binary: Base 2, symbols used: {0, 1}. Hexadecimal: Base 16, symbols used: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F}.
PGDCA Binary Octal Hexadecimal Conversions Important Questions 2026-27
Q2. Convert the Binary number (10110)2 to its Decimal equivalent. [2 Marks]
Answer: (10110)2 = (1 * 2^4) + (0 * 2^3) + (1 * 2^2) + (1 * 2^1) + (0 * 2^0)
= 16 + 0 + 4 + 2 + 0
= (22)10
Q3. Explain why the Hexadecimal Number System is widely used in computing. [3 Marks]
Answer:
- Human Readability: Binary strings (e.g., 110101101011_2) are long and error-prone for human programmers to read or write.
- Easy Conversion: Exactly 4 binary bits map cleanly to $1 hexadecimal digit (2^4 = 16).
- Compact Address Representation: Used to represent main memory addresses, system color codes (HEX
#FFFFFF), and MAC addresses in a compact format.
PGDCA Binary Arithmetic and Complements Solutions
Q4. Convert the Decimal number (25)_{10} into Binary. [2 Marks]
Answer:
- 25 \ 2 = 12, Remainder = 1
- 12 \ 2 = 6, Remainder = 0
- 6 \ 2 = 3, Remainder = 0
- 3 \ 2 = 1, Remainder = 1
- 1 \ 2 = 0, Remainder = 1Reading remainders bottom-to-top: (11001)_2
Number System PGDCA Syllabus Question Answer
Q5. Summarize the 4 primary Number Systems used in Computer Science. [3 Marks]
Answer:
| Number System | Base / Radix | Digits / Symbols | Application |
| Binary | 2 | 0, 1 | Digital electronic circuits |
| Octal | 8 | 0–7 | Shorthand grouping of 3 bits |
| Decimal | 10 | 0–9 | Human user interfaces |
| Hexadecimal | 16 | 0–9, A–F | Memory addressing & color values |
🔢 PGDCA Exam Preparation Notice: This page provides curated PGDCA (Post Graduate Diploma in Computer Applications) Number System Study Material & Solutions updated for the 2026–27 academic session. This complete guide features step-by-step base conversion formulas, binary addition/subtraction workflows, 1’s & 2’s complement techniques, positional value breakdowns, and high-yield exam questions designed to help you secure top marks in your semester examinations.
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