程序代写代做代考 computer architecture Computer Architecture

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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