A combinational circuit is defined as the functions

$F_1(A, B, C) = Σ(1, 2, 4, 7)$
$F_2(A, B, C) = Σ(3, 5, 6, 7)$

Derive the PLA program table for this circuit.

Question

A combinational circuit is defined as the functions

[latex]F_1(A, B, C) = Σ(1, 2, 4, 7)[/latex]
[latex]F_2(A, B, C) = Σ(3, 5, 6, 7)[/latex]

Derive the PLA program table for this circuit.

Accepted Answer

[latex]F_1(A, B, C) = Σ(1, 2, 4, 7) = \bar{A}\bar{B}C +\bar{A}B\bar{C} + A\bar{B}\bar{C} + ABC[/latex]
[latex]F_2(A, B, C) = Σ(3, 5, 6, 7) = \bar{A}BC + A\bar{B}C + AB\bar{C} + ABC[/latex]

The K-maps for [latex]F_1[/latex] , [latex]\bar{F}_1[/latex] , [latex]F_2[/latex] , and [latex]\bar{F}_2[/latex] are shown below.

[latex]F_1=\bar{A}\bar{B}C+\bar{A}B\bar{C}+A\bar{B}\bar{C}+ABC[/latex]

[latex]\bar{F}_1=\bar{A} \bar{B} \bar{C}+\bar{A}BC+AB\bar{C}+\bar{A}B\bar{C}[/latex]

[latex]F_2=AB+AC+BC[/latex]

[latex]\bar{F}_2=\bar{A}\bar{B}+\bar{A}\bar{C}+\bar{B}\bar{C}[/latex]

Examination of [latex]F_1[/latex] , [latex]\bar{F}_1[/latex] , [latex]F_2[/latex] , and [latex]\bar{F}_2[/latex] reveals that no matter which combination we select, we will have seven distinct product terms. So, we choose [latex]F_1[/latex] and [latex]F_2[/latex] and the PLA program table is shown below.

	Product Term	Inputs			Outputs
	Product Term	A	B	C	[latex]F_1[/latex]	[latex]F_2[/latex]
AB	1	1	1	_	_	1
AC	2	1	_	1	_	1
BC	3	_	1	1	_	1
[latex]\bar{A} \bar{B} C[/latex]	4	0	0	1	1	_
[latex]\bar{A} B\bar{C} [/latex]	5	0	1	0	1	_
[latex]A\bar{B}\bar{C}[/latex]	6	1	0	0	1	_
ABC	7	1	1	1	1	_
					T	T	T/C

Question 11.EX.1: A combinational circuit is defined as the functions F1(A, B,...

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