Fundamentals of Digital Logic and Microcontrollers, 6th Edition

Questions and Problems

3.1 Perform the following operations. Include your answers in hexadecimal. A6₁₆ OR 31₁₆; F7A₁₆ AND D80₁₆; 36₁₆ ⊕ 2A₁₆

3.2 Given A = 1001₂, B = 1101₂, find: A OR B; B A; ; A ⊕ A.

3.3 Perform the following operation: A7₁₆ ⊕ FF₁₆. What is the relationship of the result to A7₁₆?

3.4 Draw a logic diagram to implement F = ABCDE using only 3-input AND gates.

3.5 Draw a logic diagram using two-input AND and OR gates to implement the following function F = P(P + Q)(P + Q + R)(P + Q + R + S) without any simplification; then analyze the logic circuit to verify that F = P.

3.6 Prove the following identities algebraically and by means of truth tables:

3.7 Simplify each of the following Boolean expressions as much as possible using identities:

1. (a
2. (b
3. (c
4. (d
5. (e
6. (f)
7. (g