Decimal number system 

The number system with a base of 10 meaning has ten elements or symbols is called the decimal number system. The 10 elements of the decimal number system are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Each digit in the decimal number system has its position value, and every next digit is ten times more significant than the previous one. For example, we take 65; then six is ten times more significant than 5.

(56)₁₀ = (5 x 10¹) + (6 x 10⁰)

(78)₁₀ = (7 x 10¹) + (8 x 10⁰)

(491)₁₀ = (4 x 10²) + (9 x 10¹) + (1 x 10⁰)

Binary number system

The number system with a base of 2, meaning two elements or symbols is called the binary number system. For example, the two elements of the decimal number system are 0,1. This number system is mainly used as a machine language for computers to understand. Every digit in a binary number is called a bit. A bit is a single binary digit.

1001 is a four-bit binary number

101100 is a six-bit binary number

100 is a three-bit binary number

Binary number table

Advantages of using decimal number system

• Used by humans
• Easy to read
• Easy to work on

Disadvantages of using decimal number system

• Takes up too much space
• Time taking in solving the problems
• Digital system is based on binary number system
• Decimal and hexadecimal take up the same space of 4 bit each but hexadecimal can store more digits in it.

Decimal to binary number system

To convert from decimal number system to binary number system, we divide the number by 2 and note the remainder each time until no more division is possible, and read it in reverse order, i.e. from LSB (least significant bit) to the MSB (Most significant bit).

Example 1: convert (56)₁₀ into a binary equivalent number

Solution:

Given number is 56

56 / 2 = 26 remainder = 0 (MSB)

26 / 2 = 13 remainder = 0

13 / 2 = 6 remainder = 1

6 / 2 = 3 remainder = 0

3 / 2 = 1 remainder = 1

1 / 2 = 0 remainder = 1 (LSB)

The binary equivalent of 56 is

(56)₁₀ = (110100)₂

Example 2: convert (115)₁₀ into a binary equivalent number

Solution:

Given number is 56

115 / 2 = 57 remainder = 1 (MSB)

57 / 2 = 28 remainder = 1

28 / 2 = 14 remainder = 0

14 / 2 = 7 remainder = 0

7 / 2 = 3 remainder = 1

3 / 2 = 1 remainder = 1

1 / 2 = 0 remainder = 1 (LSB)

The binary equivalent of 56 is

(115)₁₀ = (1110011)₂