Question 4 - 3 Mark Questions - Chapter 2 Class 11 - Encoding Schemes and Number System

Convert following binary numbers to decimal:

(a) 1010

(b) 1101101010

Answer:

• 1010  

1010 ₂ = 1 x 2 ³ + 0 x 2 ² + 1 x 2 ¹ + 0 x 2 ⁰  

           =  8 + 0 + 2 + 0

           = (10) ₁₀

• 1101101010

1101101010 ₂ = 1 x 2 ⁹ + 1 x 2 ⁸ + 0 x 2 ⁷ + 1 x 2 ⁶ + 1 x 2 ⁵ + 0 x 2 ⁴ + 1 x 2 ³ + 0 x 2 ² + 1 x 2 ¹ + 0 x 2 ⁰  

                          = 512 + 256 + 0 + 64 + 32 + 0 +  8 + 0 + 2 + 0 

                       = (874) 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.