Design a circuit with optimum utilization of PLA to implement the following functions F1= $\sum m(0,2,5,8,9,11), F2=\sum m(1,3,8,10,13,15), F3=\sum m(0,1,5,7,9,12,14).$

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written 7.7 years ago by

ANS : 1) K-MAPS and simplification For F1 consider it as F1(A,B,C,D) enter image description here

F1=$\bar{\mathbb{A}}~\overline{\mathbb{B}}~\overline{\mathbb{D}}~+~\bar{\mathbb{B}}~\overline{\mathbb{C}}~\overline{\mathbb{D}}~+~A\overline{\mathbb{B}}~\overline{\mathbb{D}}~+~\bar{\mathbb{A}}~B~\overline{\mathbb{C}}~D$

For F2,

enter image description here

F2=$\bar{\mathbb{A}}~\overline{\mathbb{B}}~D~+~A~B~D~+~A~\overline{\mathbb{B}}~\overline{\mathbb{D}}$

For F3,

enter image description here

2) PLA Programming table:-

PRODUCT TERM NO.	PRODUCT TERM	INPUTS				OUTPUTS
A	B	C	D	F1	F2	F3
1	$\bar{\mathbb{A}}~\overline{\mathbb{B}}~\overline{\mathbb{D}}$	0	0	-	0	1	-	-
2	$\bar{\mathbb{B}}~\overline{\mathbb{C}}~\overline{\mathbb{D}}$	-	0	0	0	1	-	-
3	$A~\overline{\mathbb{B}}~D$	1	0	-	0	1	-	-
4	$\bar{\mathbb{A}}~B~\overline{\mathbb{C}}~D$	0	1	0	1	1	-	-
5	$\bar{\mathbb{A}}~\overline{\mathbb{B}}~D$	0	0	-	1	-	1	-
6	$A~B~D$	1	1	-	1	-	1	-
7	$A~\overline{\mathbb{B}}~\overline{\mathbb{D}}$	1	0	-	0	-	1	-
8	$\bar{\mathbb{A}}~\overline{\mathbb{B}}~\overline{\mathbb{C}}$	0	0	0	-	-	-	1
9	$\bar{\mathbb{B}}~\overline{\mathbb{C}}~D$	-	0	0	1	-	-	1
10	$\bar{\mathbb{A}}~B~D$	0	1	-	1	-	-	1
11	$A~B~\overline{\mathbb{D}}$	1	1	-	0	-	-	1

3) Implementation of logic circuit :

enter image description here

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