Question

Q2. [60 marks] A logical function is realized by the combination of NAND and NOR gates with the ircuit connections shown in Figure1. a. [20 points] Find the Boolean expression of the function F b. [20 points] Simplify the Boolean expression using Boolean Algebra; c. [20 points] Re-design the circuit using the least NAND-only gates (each NAND has 2 inputs). F(A,B,C) Figure 2: Logical circuit with NAND and NOR.

Answer 1

Logic circuit with NAND and NOR Part(A): - rightarrow Redraw logic circuit for solving: - Now F = (A middot X^bar middot A + X^bar)^bar = A middot X^bar^bar + A + x^bar^bar = A middot X + A + X So F = [AX + A + X] (1) Now X = (A middot b)^bar + (B + C)^bar^bar = A middot B^bar^bar middot B + C^bar^bar = (A B) (B + C) = AB + ABC = AB(1 + C) X = AB (2) Now by eq^n (1) & (2) F = S(AB) + A + AB = AB(A + 1) + A F = AB + A F = A(B + 1) F = A part-(B): - Boolean expression is already simplified leftarrow Here F = (AX + A + X) where X = AB + ABC = (AB) F = A(AB + ABC)