NUMBER SYSTEM

When we type letters, words, or other information, the computer converts them into numerical forms because computers process data using numbers.

A computer understands positional number systems, in which a limited number of symbols, called digits, are used.

The value of a digit depends on:

1. The digit itself.
2. The position of the digit in the number.
3. The base of the number system.

Base: The total number of digits available in a number system.

MAJOR NUMBER SYSTEMS

Number System	Base	Digits Used
Binary	2	0, 1
Octal	8	0–7
Decimal	10	0–9
Hexadecimal	16	0–9 and A–F

DECIMAL NUMBER SYSTEM

The Decimal Number System is the number system used in our everyday life.

It has a base of 10 and uses ten digits:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

In the decimal number system, the positions to the left of the decimal point represent:

Thousands   Hundreds   Tens   Units

    │           │         │      │

   10³         10²       10¹    10⁰

BINARY NUMBER SYSTEM

The Binary Number System is the fundamental number system used by computers.

Characteristics

• Uses two digits: 0 and 1.
• Also known as the Base-2 Number System.
• Each position represents a power of 2.
• The rightmost position represents 2⁰.

Binary Positions:

   2³    2²    2¹    2⁰

    │     │     │     │

    8     4     2     1

OCTAL NUMBER SYSTEM

The Octal Number System uses eight digits:

0, 1, 2, 3, 4, 5, 6, 7

Characteristics

• Has a base of 8.
• Uses digits from 0 to 7.
• Each position represents a power of 8.
• The rightmost position represents 8⁰.

Octal Positions:

   8³    8²    8¹    8⁰

HEXADECIMAL NUMBER SYSTEM

The Hexadecimal Number System has a base of 16.

It uses:

• Ten digits: 0–9
• Six letters: A–F

Hexadecimal Values

Symbol	Value
A	10
B	11
C	12
D	13
E	14
F	15

Characteristics

• Also known as the Base-16 Number System.
• Uses 16 symbols: 0–9 and A–F.
• Each position represents a power of 16.
• The rightmost position represents 16⁰.

Hexadecimal Digits:

0  1  2  3  4  5  6  7  8  9  A  B  C  D  E  F

                                   │  │  │  │  │  │

                                  10 11 12 13 14 15

Memory Trick

B – O – D – H

Binary → Octal → Decimal → Hexadecimal

2 → 8 → 10 → 16

Practice Question

1. The binary equivalent of the decimal number 25 is
    (A) 11001
    (B) 10011
    (C) 10010
    (D) 11100

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Answer: (A) 11001

2. Which number system uses only 2 digits to represent numbers?
 (A) Decimal
 (B) Hexadecimal
 (C) Binary
 (D) Octal

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Answer: (C) Binary

3. Which of the following is a valid octal number?
 (A): F23
 (B): 296
 (C): 756
 (D): 149

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Answer: (C) 756

4. The rightmost digit in a number system is called
 (A)least significant digit (LSD)
 (B) most significant digit (MSD)
 (C) units place digit
 (D) None

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Answer: (A) least significant digit (LSD)

Explanation: In any positional number system, the digit furthest to the right represents the lowest exponent/power of the base, making it the least significant digit (or bit).

5. The decimal equivalent of (A2)16 is
 (A) 162
 (B) 120
 (C) 100
 (D) 172

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Answer: (A) 162
Explanation: In base-16, ‘A’ represents 10. Expanding it out: (10 × 16^1) + (2 × 16^0) translates to 160 + 2 = 162.

6. Which of the following number systems also uses letters to represent digits of a number?
 (A) Hexadecimal
 (B) Octal
 (C) Binary
 (D) Decimal number system

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