NUMBER SYSTEM

IN COMPUTER SCIENCE

PREPARED BY Ashad Javed

SUBJECT Computer Science

0101 1010

0xFF · 0b1010 · 0o17 · 42

02

What is a Number System?

A number system is a mathematical notation for representing numbers using a consistent set of digits or symbols.

Defines how numbers are stored and processed
Each system has a base (radix)
Computers use binary at hardware level
Humans use decimal in daily life

CPU

1

0

1

Binary
Base 2

→

Octal
Base 8

→

Decimal
Base 10

→

Hexadecimal
Base 16

03

Binary Number System

⚡

Base-2 System

Uses only 0 and 1

Each digit is called a BIT (Binary Digit)
8 bits = 1 Byte
Represents OFF (0) and ON (1)
Foundation of all digital computing

Example: (1010)₂ = 10 in Decimal

1

0

1

0

1

0

1

1 Byte = 8 Bits

04

Binary Conversion

Decimal 13 → Binary

Number÷ 2QuotientRemainder

13÷ 261

6÷ 230

3÷ 211

1÷ 201

↑ Read remainders bottom to top

Result: (13)₁₀ = (1101)₂

Place Value Verification

2³

8

1

8×1=8

2²

4

1

4×1=4

2¹

2

0

2×0=0

2⁰

1

1×1=1

8 + 4 + 0 + 1 = 13 ✓

05

Octal Number System

🔢

Base-8 System

Uses digits 0 – 7

Prefix: 0 (e.g., 017)
Each octal digit = 3 binary bits
Used in Unix file permissions
Compact representation of binary

Example: (17)₈ = 15 in Decimal

OCT

0

1

2

3

4

5

6

7

Unix Permissions

7 111 rwx

5 101 r-x

4 100 r--

06

Decimal Number System

🌍

Base-10 System

Uses digits 0 – 9

Most natural for humans
Based on 10 fingers (deci = ten)
Each position is a power of 10
Standard in everyday mathematics

Example: 425 = 4×10² + 2×10¹ + 5×10⁰

000

Counting in Decimal

10²

Hundreds

4

10¹

Tens

2

10⁰

Units

5

07

Hexadecimal Number System

💻

Base-16 System

Uses 0–9 and A–F

Prefix: 0x (e.g., 0xFF)
Each hex digit = 4 binary bits
Used in memory addresses, colors
Compact binary representation

Example: (1F)₁₆ = 31 in Decimal

10A1010

11B1011

12C1100

13D1101

14E1110

15F1111

#FF3CAC

#CCFF00

#00BFFF

08

Conversion Table

Decimal	Binary	Octal	Hexadecimal
0	0000	0	0
1	0001	1	1
2	0010	2	2
3	0011	3	3
4	0100	4	4
5	0101	5	5
6	0110	6	6
7	0111	7	7
8	1000	10	8
9	1001	11	9
10	1010	12	A
11	1011	13	B
15	1111	17	F
16	10000	20	10

09

Real-World Applications

🖥️

Binary

CPU logic gates
RAM storage
Digital circuits

🔐

Octal

Unix permissions
File systems
Legacy systems

🧮

Decimal

User interfaces
Financial data
Human I/O

🎨

Hexadecimal

Memory addresses
HTML/CSS colors
MAC addresses

Memory Address Example: 0x7FFF5FBFF8A0

10

Summary & Thank You

BINARY

Base 2

Digits: 0, 1

Hardware level

OCTAL

Base 8

Digits: 0–7

File permissions

DECIMAL

Base 10

Digits: 0–9

Human use

HEX

Base 16

Digits: 0–9, A–F

Memory & colors

THANK YOU

Prepared by Ashad Javed

01000001 01110011 01101000 01100001 01100100