This is '4 bit Magnitude Comparator' assignment of
Digital Design  Computer Engineering of
Somaiya University  Gyaani Buddy
The comparison of two numbers is an operator that determines one number is greater than, less than (or) equal to the other number. A magnitude comparator is a combinational circuit that compares two numbers A and B and determines their relative magnitude. The outcome of the comparator is specified by three binary variables that indicate whether A>B, A=B (or) A<B.
Two Bit Magnitude Comparator Implementation Details:
Truth Table
A1

A0

B1

B0

A > B

A = B

A < B








0

0

0

0

0

1

0








0

0

0

1

0

0

1








0

0

1

0

0

0

1








0

0

1

1

0

0

1








0

1

0

0

1

0

0








0

1

0

1

0

1

0








0

1

1

0

0

0

1








0

1

1

1

0

0

1








1

0

0

0

1

0

0


0






1

0

0

1

1

0

0

1







1

0

1

0

0

1

0








1

0

1

1

0

0

1


11






1

1

0

0

1

0

0

1







1

1

0

1

1

0

0








1

1

1

0

1

0

0








1

1

1

1

0

1

0








From the Truth Table:
(A<B) = A1’B1 + A0’B1B0 +A1’A0’B0
(A=B) = A1’A0’B1’B0 ’+ A1’A0 B1’B0 +A1A0B1B0 + A1A0’B1B0’
=A1’B1’ (A0’B0’ +A0B0) + A1B1 (A0B0+A0’B0’)
= (A0B0+A0’B0’) (A1B1+A1’B1’)
= (A0 EXNOR B0) (A1 EXNOR B1)
(A>B) = A1B1’ + A0B1’B0 ’+A1A0B0’
Logic Diagram of 2 bit Comparator
Four Bit Magnitude Comparator Implementation Details
Pin Diagram of IC 7485
Logic Diagram of IC 7485
Comparing Table
This is '4 bit Magnitude Comparator' assignment of
Digital Design  Computer Engineering of
Somaiya University  Gyaani Buddy
1. Design a 1 bit magnitude comparator using logic gates.
Ans 1:A comparator used to compare two bits is called a single bit comparator. It consists of two inputs each for two single bit numbers and three outputs to generate less than, equal to and greater than between two binary numbers.
Truth Table:
A>B = AB’
A<B = A’B
A=B = A’B’ +AB
THUS:
(A>B) + (A<B) = A’B + AB’
NOW TAKE COMPLEMENT BOTH SIDES
((A>B) + (A<B))’ =( A’B + AB’)’
((A>B) + (A<B))’ = AB’ + A’B
((A>B) + (A<B))’ = (A+ B’) (A’ + B)
((A>B) + (A<B))’ =( AA’ +AB + A’B’ +BB’)
((A>B) + (A<B))’= (AB +AB’)