Question

5, [points] This problem covers floating-point IEEE format. (a) Assuming single precision IEEE 754 format, what is the binary pattern for decimal number -6.16? (b) Assuming single precision IEEE 754 format, what decimal number is represented by this word: 0 01111100 01100000000000000000000 (Hint: remember to use the biased form of the exponent.)

Answer 1

Solution

(a)

0110. 0010 1000 1111 0101 1100 0010 1000 1111 0101 1100 …...

01.10 0010 1000 1111 0101 1100 0010 1000 1111 0101 1100 * 22

Fraction =

10 0010 1000 1111 0101 1100 0010 1000 1111 0101 1100

Exponent =

2+127

= 129

We already know it is positive the sign bit is zero(0)

The bit pattern=

01000 0001 10 0010 1000 1111 0101 1100 0010 1000 1111 0101 1100

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(b)

Sign bit: 0

Exponent: 125 - 127 = -2

Fraction: 01100000000000000000000

= (+1)* (2^(125-127))*(1.001)₂

= (+1)*(0.25)*(0.125)

= 0.03125

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all the best