Floating Point Assume a 12 bit floating point representation which uses the firs
ID: 669790 • Letter: F
Question
Floating Point
Assume a 12 bit floating point representation which uses the first bit as a sign bit, the next 6 for the exponent and the last 5 for the fraction. The bias is 31. Fill in the table below.
Bit representation
e
E
f
M
V
0 010110 10011
1 100101 10110
0 000000 10110
1
38/32
48.0
11/32
What is the bit sequence and value for the largest possible normalized value?
What is the bit sequence and value for the smallest possible (non-zero) positive normalized value?
What is the bit sequence and value for the largest possible de-normalized value?
What is the bit sequence and value for the smallest possible (non-zero) positive de-normalized value?
Bit representation
e
E
f
M
V
0 010110 10011
1 100101 10110
0 000000 10110
1
38/32
48.0
11/32
Explanation / Answer
Solving for 0 010110 10011:
Signbit= 0(positive)
Exponent(or e)= 010110(base 2) or 22(base 10)
E=exp-bias
=22-31
=-9
Frac (or f) = 10011
=(1 * 0.5)+(0*0.25)+(0*0.125)+(1*0.0625)+(1*0.03125)
=0.5+0+0+0.0625+0.03125
= 0.59375
M=1+frac = 1+ 0.59375 =1.59375
Bit representation
e
E
f
M
V
0 010110 10011
1 100101 10110
0 000000 10110
1
38/32
48.0
11/32
Bit representation
e
E
f
M
V
0 010110 10011
22 -9 0.59375 1.593751 100101 10110
0 000000 10110
1
38/32
48.0
11/32
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