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Digital Logic Design (CS302)
Assignment # 03
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Total marks
= 20
Deadline
Date
19th
January, 2016
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Question Statement:
You are provided
with a figure that represents 4x3 PLA. You have to find out:
I.
Boolean expression for P1, P2, P3, P4, P5 & P6.
II.
Boolean expression for Final Outputs O1, O2 & O3 OR Gates
III.
Convert all Boolean expressions (P1, P2, P3, P4, P5, P6, O1, O2 & O3)
into ABEL expressions/equations.
Figure 1
Solution:
A̅ B̅ C̅ D̅ A B C D
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P1= A.B̅.D̅
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P2= A.B̅.C̅.D
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P3= A̅.B.C.D̅
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P4= A̅.B̅
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P5= A̅.B̅.C̅
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P6= A.B̅.C̅.D
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O1=
P1+P3+P4+P6
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O1=
A.B̅.D̅ + A̅.B.C.D̅+
A̅.B̅ + A.B̅.C̅.D
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O2=
P2+P4+P6
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O2=
A.B̅.C̅.D+ A̅.B̅+ A.B̅.C̅.D
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O3=
P1+P3+P6
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O3=
A.B̅.D̅+ A̅.B.C.D̅+
A.B̅.C̅.D
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Now
writing expression in ABEL
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Boolean Exp.
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ABEL EXP
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P1= A.B̅.D̅
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P1= A&!B&!D
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P2= A.B̅.C̅.D
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P2= A&!B&!C&D
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P3= A̅.B.C.D̅
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P3= !A&B&C&!D
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P4= A̅.B̅
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P4= !A&!B
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P5=
A̅.B̅.C̅
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P5=
!A&!B&!C
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P6= A.B̅.C̅.D
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P6= A&!B&!C&D
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Boolean
Exp
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ABEL Exp
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O1=
P1+P3+P4+P6
O1= A.B̅.D̅ + A̅.B.C.D̅+ A̅.B̅ + A.B̅.C̅.D
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O1=
P1#P3#P4#P6
O1= A&!B&!D#!A&B&C&!D#!A&!B# A&!B&!C&D
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O2=
P2+P4+P6
O2=
A.B̅.C̅.D+ A̅.B̅+ A.B̅.C̅.D
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O2= P2#P4#P6
O2= A&!B&!C&D#!A&!B# A&!B&!C&D
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O3=
P1+P3+P6
O3=
A.B̅.D̅+ A̅.B.C.D̅+
A.B̅.C̅.D
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O3=
P1#P3#P6
O3= A&!B&!D#!A&B&C&!D# A&!B&!C&D
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