Homework #2 Computer Organization
1. Convert -87.375
10
to its 64-bit IEEE-754 floating point representation.
2. Suppose A, B and C are 32-bit IEEE 754 floating point variables with A having a normalized value of 1.11
2
x
2
75
and B having a normalized value of 1.101
2
x 2
40
. After the assignment statement "C = A+B", why is C's value
equal to A's value and not the “mathematically correct” sum?
3. For the same values of A and B in question 2, would the sum be correct if A, B, and C used a 64-bit IEEE 754
floating point format? (explain your answer)
4. What is the smallest, positive normalized 32-bit IEEE 754 floating point value?
5. What is the largest, positive denormalized 32-bit IEEE 754 floating point value?
6. What is the smallest, positive denormalized 32-bit IEEE 754 floating point value?
7.
For the Boolean function F represented in the above truth table:
a) write the unsimplified sum-of-products (SOP) Boolean expression
b) draw the unsimplified circuit for this SOP expression. Also, determine the number of gate delays and circuit
complexity (# gates + # inputs into those gates)
c) using the identities of Boolean algebra (or a K-map) , simplify this function F as much as you can
d) draw the simplified circuit for your answer in part (c). Also, determine the number of gate delays and circuit
complexity (# gates + # inputs into those gates) of this circuit
Name:____________________
1
111
0
011
0
101
1
001
0
110
0
010
1
100
1
000
FCBA
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