Combination Circuits

Q3: Implement equations using Half Adders

Q- Implement the following equations using only Half Adder circuits.

D= A XOR B XOR C

E = A’BC + AB’C

F = ABC’ + (A’+B’) C

G= ABC

Ans: We know the equations for Half Adder are

S = A xor B           and        C = AB

And can be represented as follow:

We have 3 inputs A, B, C and we need D= A xor B xor C

So we connect 2 HA as below to get D

And the other output of 2nd adder is (A XOR B) C = A’BC+ AB’C which is actually E

Now we need F = ABC’ + (A’ + B’) C

which can be written as F = AB C’ + (AB)’ C = (AB) XOR C hence connect carry output of 1st adder (which is AB) with input C as follow:

And we get G= ABC at the other end.

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