Determine the IEEE standard 32-bit binary representation for each of the followi

Question

Determine the IEEE standard 32-bit binary representation for each of the following float values: Show all of your work and include a few comments as to what you are doing at each step. 2, 015.3 -111.3125 Convert each of the following 32 IEEE 754 single precision bit patterns to its corresponding decimal value (the bits are separated into groups of 4 to make interpretation easier). Show all of your work and include a few comments as to what you are doing at each step. 1011 1101 1011 0000 0000 0000 0000 0000 0100 0110 1110 0000 0000 0000 0000 0000

Explanation / Answer

Multiple Questions : Answering one (Question 8)

a. 1011 1101 1011 0000 0000 0000 0000 0000 = 1 01111011 01100000000000000000000

sign bit = 1 => negative

exp : (01111011)2 = (123)10

exp = bias + p

123 = 127 + p => p = -4

1.01100000000000000000000=> -(0.0001011)2 = (-0.0859375)10

b. 0100 0110 1110 0000 0000 0000 0000 0000 = 0 10001101 11000000000000000000000

sign bit = 0 => positive

exp : (10001101)2 = (141)10

exp = bias + p

141 = 127 + p => p = 14

1.11000000000000000000000 => (111000000000000)2 = (28672)10

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