7.1 Boolean Algebra Structure 1. Give reasons for the following steps in the pro
ID: 2901524 • Letter: 7
Question
7.1 Boolean Algebra Structure
1. Give reasons for the following steps in the proof sequence:
(x + y)(x' + y) = (y + x)(y + x') ________________
= y + (xx') _____________________
= y + 0 _________________________
= y ____________________________
2. Give reasons for the following steps in the proof sequence:
(x + y) + (yx') = (y + x) + (yx') ________________
= y + (x + (yx')) ________________
= y + (x + y)(x + x') _____________
= y + (x + y)1 _________________
= y + (x + y) ___________________
= (x + y) + y ____________________
= x + (y + y) ____________________
= x + y ________________________
3. Give the Boolean expression for the network on p 567, #2.
__________________________________________________
4. Give the truth function for the network on p 567, #2.
5. Find the canonical sum-of-products form for the truth function given below.
X1 | X2 | X3 | f(X1, X2, X3)
1 1 1 0_____
1 1 0 1_____
1 0 1 1_____
1 0 0 0_____
0 1 1 1_____
0 1 0 0_____
0 0 1 0_____
0 0 0 1_____
Answer:__________________________________________________________________________
Explanation / Answer
1. Commutative law
Distributive law and then idempotent law y.y=y
Identity function in OR operation
2. Commutative law
Associative law
Distributive law
x +x'=1(OR operation with negation)
Anything ANDed with one is itself
Associative property
Antthing ANDed or ORed with itself is itself
[Need diagrams for the two questions]
5. For finding Sum of Products or SOP, find out the entries which are one and the corresponding variables in those entries will be ANDed together with their high states as the variable and their low states written as variable'.
Here, X1X2X3' + X1X2'X3 + X1'X2X3 + X1'X2'X3'
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