Question 7 - 3 Mark Questions - Chapter 2 Class 11 - Encoding Schemes and Number System

Convert 1C6A ₁₆ to

(a) Decimal

(b) Binary

Answer:

1C6A ₁₆

1. Decimal

1C6A ₁₆ = 1 x 16 ³ + 12 x 16 ² + 6 x 16 ¹ + 10 x 16 ⁰  

= 4096 + 3072 + 96 + 10

= 7274 ₁₀

Explanation:

• To obtain the decimal equivalent of a hexadecimal number, individual digits of hexadecimal number should be multiplied by powers of 16 starting with rightmost digit multiplied by 16 ⁰ , second last digit multiplied by 16 ¹ , third last digit multiplied by 16 ² and so on up to the leftmost digit. 
• For digits after the decimal point, the leftmost digit should be multiplied by 16 ^-1 and the next digit by 16 ^-2 and so on up to the rightmost digit.

• For alphabets A to F, the corresponding codes should be multiplied with the respective power of 16.

Here,

• A = 10
• B = 11
• C = 12
• D = 13
• E = 14
• F = 15  

b. Binary

1C6A ₁₆

Therefore, 1C6A ₁₀ = 0001110001101010 ₂

Explanation:

• To obtain the binary equivalent of a hexadecimal number, individual digits of the hexadecimal number should be converted to binary in groups of four digits as given in the table below.