Question 1 - 5 Mark Questions - Chapter 2 Class 11 - Encoding Schemes and Number System

Do as directed:

(a) Convert the Decimal number 781 to its Binary equivalent.

(b) Convert Binary number 101101.001 to its decimal equivalent

(c) Convert Octal number 321.7 info its Binary equivalent

Answer:

(a) 781 ₁₀ to its binary equivalent

Therefore, 781 ₁₀ = 1100001101 ₂

Explanation:

• Repeatedly divide the decimal number by 2 until the quotient becomes 1 and record all the remainders. 
• The remainders should be written bottom to upwards to get the binary equivalent of the decimal number.

(b) 101101.001 ₂ to its decimal equivalent

        101101.001 = 1 x 2 ⁵ + 0 x 2 ⁴ + 1 x 2 ³ + 1 x 2 ² + 0 x 2 ¹ + 1 x 2 ⁰ + 0 x 2 ^-1 + 0 x 2 ^-2 + 1 x 2 ^-3

                            = 32 + 0 + 8 + 4 + 0 + 1 + 0 + 0 + 0.125

                = 45.125 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.

(c)    321.7 ₈ to its binary equivalent

      Therefore, 321.7 ₈ = 11010001.111 ₂

Explanation:

• To obtain binary equivalent of an octal number, individual digits of octal number should be converted to binary in groups of three digits as given in the table below.