Question

3. Design a one bit subtractor. The circuit subtracts the number Y from X and generates a difference D bit and a borrow out Bo bit. The circuit has three inputs: X, Y and borrow in bit Bi shown in the figure below: во ID a. Derive the truth table for the function D(X,Y,Bi) and Bo(X,Y,Bi) b. Write the functions D and Bo as a canonical SOP form, using the little m notation. c. To implement the functions D and Bo on a PLA what is the minimum number of different product terms needed? Give the product terms. Show how to implement D and Bo on the following PLA, using the minimum number of product terms. 00000000

Answer 1

Answer is as follows :

Answer A :

Truth Table For given Scenario :

INPUT OUTPUT

Answer B :

Canonical SOP Forms ;

D = X'Y'Bi + X'YBi' + XY'Bi' + XYBi

Bo = X'Y'Bi + X'YBi' + X'YBi + XYBi

or in little m notation :

D = m( 1,2,4,7)

Bo = m ( 1,2,3,7)

Answer C :

For D, we need following Product terms :

X'Y'Bi , X'YBi' , XY'Bi' , XYBi (1,2,4,7)

For Bo,we need following Product terms :

X'Y'Bi , X'YBi' , X'YBi , XYBi (1,2,3,7)

Out of which (1,2,7) are same and (3,4) are different.

So we need total of 5 product terms i.e. :

X'Y'Bi , X'YBi' , XYBi , XY'Bi' , X'YBi

Answer D

Circuit on PLA :

Bo

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