Information and Communication Technology

Binary number system

The binary number system is exactly like the decimal number system, except the base is 2, instead of 10. We have only two symbols or digits (0 and 1), which can be used in this number system. The largest single digit is 1. Each position in a binary number represents a power of the base 2. Hence in this system, the rightmost position is the units (2⁰) position, the second position from the right is the 2’s (2¹⁾ position , and proceeding this way we have 4’s ( 2²) position, 8’s (2 ³) position, .. and so on. Therefore , the decimal equivalent of the binary number 10101 (written as (10101)₂ ) is :

(1 x 2 ⁴ ) + (0 x 2³) + (1 x 2²) + (0 x 2¹) + (1 x 2⁰) = 16 + 0 + 4 + 0 + 1 = 21

Hence we write 10101₂ = 21₁₀