Express the following numbers in IEEE 32-bit floating point format 3 8 -15 -1.75
ID: 3881520 • Letter: E
Question
Express the following numbers in IEEE 32-bit floating point format
3
8
-15
-1.75
128
-1/64
The following numbers use the IEEE 32-bit floating point format. Find the equivalent decimal value.
0 01110011 10000000000000000000000
1 01111100 00000000000000000000000
0 11100001 11000000000000000000000
1 10000011 11100000000000000000000
Find one integer that cannot be represented in 24-bit 2’s complement notation. Explain why not. Find one floating point number that cannot be represented in IEEE 32-bit format. Explain why not.
3
8
-15
-1.75
128
-1/64
Explanation / Answer
The representation are
3 01000000 01000000 00000000 00000000
8 01000001 00000000 00000000 00000000
-15 11000001 01110000 00000000 00000000
-1.75 10111111 11100000 00000000 00000000
128 01000011 00000000 00000000 00000000
-1/64 10111100 10000000 00000000 00000000
Q2
a)
0.0003662109375
b)
5.5459714*10^29
c)
-30.0
Q3
for this we cannot represent -2^23-1 with 2's complement notation as it is not in range of a 2's complement number
We cannot the represent the number which will have biased exponent greater than 255 as the exponent can't be represented in 8 bits
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