Given A 1100 0001 1101 1101 1000 0000 0000 00002 and assumi

Given A = (1100 0001 1101 1101 1000 0000 0000 0000)₂ and assuming A is a single precision IEEE-754 floating point number, what decimal value does A represent? Show A in normalized scientific notation: 1.X * 2^y.

Convert (31.8)₁₀ to IEEE-754 single-precision binary.

Given X = (0100 0001 0110 1110 0000 0000 0000 0000)2 and Y = (0100 0001 1011 1100 0000 0000 0000 0000)2 in single precision IEEE-754 floating point format, perform the following operations. Show all of your work and express the final answer in single precision IEEE 754-floating point representation.

X+Y

X*Y

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

Solution

0 10000010 11011100000000000000000 in single precision decimal representation is 14.875
0 10000011 01111000000000000000000 in single precision decimal representation is 23.500

x+y ==> 14.875 + 23.5 ==> 38.375
x*y ==> 14.875 * 23.5 ==> 349.5625