Reduce the Boolean function by using 4-variable Karnaugh map, showing the various groups (i.e…
Computer Science20255 marksCase based
$F(P, Q, R, S) = \Sigma (0,1,2,5,7,8,9,10,13,15)$
(a)[4.0]
Reduce the Boolean function $F(P, Q, R, S) = \Sigma (0,1,2,5,7,8,9,10,13,15)$ by using 4-variable Karnaugh map, showing the various groups (i.e., octal, quads and pairs).
(b)[1.0]
Draw the logic gate diagram using NAND gates only for the reduced expression. Assume that the variables and their complements are available as inputs.
Draw: logic gate diagram using NAND gates only for the reduced expression
Answer
Answer (b)
AI
NAND-only (NAND-NAND) implementation of $F = QS + Q'R' + Q'S'$: one 2-input NAND gate for each product term and a 3-input NAND gate combining them, since $[(QS)' \cdot (Q'R')' \cdot (Q'S')']' = QS + Q'R' + Q'S'$ by De Morgan's law.
