It is a system of number written is base two. The digits in base two are 0 and 1.

Conversion from Decimal to Binary (Base 10 to Base 2)

**Solved Examples**

Convert 26_{10} to base 2

Solution

2 26

2 13 R 0 least significant bit (LSB)

2 6 R 1

2 3 R 0

2 1 R 1

0 R 1 most significant bit (MSSB)

∴ 26_{10} = 110102

Example 14.2

Covert 640_{10} to base two

Solution

2 640

2 320 R 0

2 160 R 0

2 80 R 0

2 40 R 0

2 20 R 0

2 10 R 0

2 5 R 0

2 2 R 1

2 1 R 0

0 R 1

∴ 640_{10} = 10100000002

The conversion is done by successive division by 2 and keeping the remainders, which are then collected together following the arrow.

**Addition in base two**

Example 14.3

Add 111102 to 11002

Solution

11110

1100

Final sum = 1010102