Computer Architecture
Tutorial 1 – Boolean Algebra – Answers
1) Write the Truth Table for the following Boolean expression: R = A • B + C’
A B C C’ A • B R = A • B + C’
0 0 0 1 0 1
0 0 1 0 0 0
0 1 0 1 0 1
0 1 1 0 0 0
1 0 0 1 0 1
1 0 1 0 0 0
1 1 0 1 1 1
1 1 1 0 1 1
2) Simply the following Boolean Expressions to its simplest form
a) R = A + A’ • B
R = (A + A’) • (A + B) Distributive Rule
= 1 • (A + B) Negation Rule
= A + B Simplification Rule
b) R = A • (A’ + B)
R = (A • A’) + (A • B) Distributive Rule
= 0 + A • B Negation Rule
= A • B Simplification Rule
c) R = (A + C) • (A • D + A • D’) + A • C + C
R = (A + C) • (A • (D + D’)) + A • C + C Distributive Rule
= (A + C) • A + A • C + C Negation Rule
= A • A + C • A + A • C + C Distributive Rule
= A + A • C + C Idempotent Rule
= A • (1 + C) + C Distributive Rule
= A + C Simplification Rule
1 . (A + C) + C
A+C+C
A+C
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