Question 5 - 3 Mark Questions - Chapter 2 Class 11 - Encoding Schemes and Number System

Convert the following fractional binary number into decimal.

1100101.10110

Answer:

(1100101.10110) ₂

=  1 x 2 ⁶ + 1 x 2 ⁵ + 0 x 2 ⁴ + 0 x 2 ³ + 1 x 2 ² + 0 x 2 ¹ + 1 x 2 ⁰ + 1 x 2 ^-1 + 0 x 2 ^-2 + 1 x 2 ^-3 + 1 x 2 ^-4 + 0 x 2 ^-5

= 64 + 32 + 0 + 0 + 4 + 0 + 1 + 0.5 + 0 + 0.125 + 0.0625  + 0 

= (101.6875) ₁₀

Explanation:

• To obtain the decimal equivalent of a binary number, individual digits of binary number should be multiplied by powers of 2 starting with the rightmost digit multiplied by 2 ⁰ , second last digit multiplied by 2 ¹ , third last digit multiplied by 2 ² and so on up to the leftmost digit.
• For digits after the decimal point, the leftmost digit should be multiplied by 2 ^-1 and the next digit by 2 ^-2 and so on up to the rightmost digit.