Magnitude Comparator

Magnitude Comparator :
A combinational circuit that compares two input bits is called magnitude comparator.It consists of two input bits and three output bits.
If the input bits are X and Y then the output bits are corresponding to one of the case, X>Y, X=Y or X<Y.
We can write a table for magnitude comparator as :

X Y    F1
(X=Y)
  F2
(X<Y)
 F3
(X>Y)
0 0 1 0 0
0 1 0 1 0
1 0 0 0 1
1 1 1 0 0

F1 =X'Y'+XY = X (Ex-NOR)Y
F2=X'Y
F3=XY'
The logic diagram for this implementation is as below:
    
 

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