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Given X = (0100 0010 0000 1111 0000 0000 0000 0000)2 and Y = (0100 0001...

Given X = (0100 0010 0000 1111 0000 0000 0000 0000)2 and Y = (0100 0001 1010 0100 0000 0000 0000 0000)2 in single precision IEEE-754 floating point numbers, perform the following operations. Show all of your work and express the final answer in single precision IEEE 754-floating point representation.

1. X+Y

2. X*Y

Hint: show each value in binary normalized scientific notation prior to performing the arithmetic. This should make following the algorithms easier.

Rubric:

Shows X and Y in normalized scientific notation

Aligns binary points

Adds aligned values

Shows final result in IEEE-754 format

Exponent arithmetic

Multiplies values correctly

Shows final result in IEEE-754 format

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Answer #1

For the above problem, we can convert X and Y to scientific notation.

X = 0100 0010 0000 1111 0000 0000 0000 0000 ==> X = 25 * 1.1171875 ==> 35.75

Y = 0100 0001 1010 0100 0000 0000 0000 0000 ==> Y = 24 * 1.28125

So Now
i. X + Y ==> 25 * 1.1171875 + 24 * 1.28125 = 24 * 2.234375 + 24 * 1.28125
= 24 * (3.515625)
= 25 * 1.7578125 (56.25)
= 0 1000 0100 110 0001 0000 0000 0000 0000
Sign Exponent mantisa
ii. X * Y ==> 25 * 1.1171875 * 24 * 1.28125 = 29 * 1.431396484375 (732.875)
= 0 1000 1000 01101110011100000000000 Sign Exponent mantisa

That was a nice question to answer
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