CS302 Digital Logic Design Assignment No 03 Solution 19th January 2016

[Vuhelper]

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.

[Vuhelper]

Solution:
A̅ B̅ C̅ D̅ A B C D

P1= A.B̅.D̅
P2= A.B̅.C̅.D
P3= A̅.B.C.D̅
P4= A̅.B̅
P5= A̅.B̅.C̅
P6= A.B̅.C̅.D

O1= P1+P3+P4+P6
O1= A.B̅.D̅ + A̅.B.C.D̅+ A̅.B̅ + A.B̅.C̅.D
O2= P2+P4+P6
O2= A.B̅.C̅.D+ A̅.B̅+ A.B̅.C̅.D
O3= P1+P3+P6
O3= A.B̅.D̅+ A̅.B.C.D̅+ A.B̅.C̅.D

Now writing expression in ABEL
Boolean Exp.
ABEL EXP
P1= A.B̅.D̅

P1= A&!B&!D
P2= A.B̅.C̅.D
P2= A&!B&!C&D
P3= A̅.B.C.D̅
P3= !A&B&C&!D
P4= A̅.B̅
P4= !A&!B
P5= A̅.B̅.C̅
P5= !A&!B&!C
P6= A.B̅.C̅.D
P6= A&!B&!C&D

Boolean Exp

ABEL Exp


O1= P1+P3+P4+P6
O1= A.B̅.D̅ + A̅.B.C.D̅+ A̅.B̅ + A.B̅.C̅.D
O1= P1#P3#P4#P6
O1= A&!B&!D#!A&B&C&!D#!A&!B# A&!B&!C&D

O2= P2+P4+P6
O2= A.B̅.C̅.D+ A̅.B̅+ A.B̅.C̅.D

O2= P2#P4#P6
O2= A&!B&!C&D#!A&!B# A&!B&!C&D

O3= P1+P3+P6
O3= A.B̅.D̅+ A̅.B.C.D̅+ A.B̅.C̅.D

O3= P1#P3#P6
O3= A&!B&!D#!A&B&C&!D# A&!B&!C&D