Combination Circuits

2-bit COMPARATOR

Similarly we can have 2 bit comparator and the table to list all the combinations at input and their corresponding outputs is as:

A             B             f (A>B)  f (A=B) f (A<B)

00           00           0              1              0

01           00           1              0              0

10           00           1              0              0

11           00           1              0              0

00           01           0              0              1

01           01           0              1              0

10           01           1              0              0

11           01           1              0              0

00           10           0              0              1

01           10           0              0              1

10           10           0              1              0

11           10           1              0              0

00           11           0              0              1

01           11           0              0              1

10           11           0              0              1

11           11           0              1              0

And we get the equations for all three outputs from the K-maps as

We can also obtain these equations orally as for A1A0 to be greater than B1B0 either A1 is greater than B1 (i.e. A1=1 & B1=0) or A1 is equal to B1 (or A1is not less than B1 i.e. (f(A1<B1))’ = (A1’B1)’= (A+ B1‘) & A0 is greater than B0 (i.e. A0=1 & B0=0).

Hence the equation we get is f (A>B) = A1B1‘+ (A1 + B1’) A0B0’ = A1B1‘+ A0 B1’B0’+ A1A0B0

We can also get the equation orally similar to the above case. Now we can implement the above equation easily. Similarly we can implement other higher comparators

257 Replies to “2-bit COMPARATOR

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