Need help solving this equation Determine the IEEE doublepre

Need help solving this equation.

Determine the IEEE double-precision and single-precision machine representation of 64.37109375. Show your work and your final answer should be composed of three parts: sign, exponent, and mantissa (use 0...0 and indicate how many zeros if the remained part is all zeros).

Solution

Single precision format:

given number is 64.37109375

first convert number into binary format

64 = > 1000000

0.37109375 => 01011111

1000000.01011111 = 1.00000001011111 * 2⁶   

sign bit = 0

exponent (8 bit) = 127+6=133=10000101

mantissa (23 bit) : 000000010111110000000

double pricicion format:

sign bit : 0

0001000000.01011111 => 0.00100000001011111 x 2⁸

exponent (11 bit) : 1023+8=1031=1000 000 000 0111

mantissa(52 bit) :00100000001011111000000 till 52 position