GATE Overflow | Mock GATE | Test 1 | Question: 14

Question

Let $S(x,y,z)$ and $C(x,y,z)$ represents the Sum & Carry function of a full adder circuit. Which of the following options best represents $S(x,y,z)$ and $C(x,y,z)$ respectively?

• A. $x \oplus y \oplus z, y( x \oplus z)+xy$
• B. $x \oplus y \oplus z, y(x+y+z)$
• C. $x \odot y \odot z, z(x+y)+xy$
• D. $\text{None of these}$

Comments

Draw truth table for XOR and XNOR for variables A,B,C and check and then tell me if still you have confusion.

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Yes got it.Thanks

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question was easy and conceptual

When there are odd number of inputs then EXOR and EX-NOR gives the same truth table, as EXOR is an ODD function it means if there are odd number of 1's in the input then the output is 1, and EXNOR is an even function, it means if there are even number of 0's in the input then output will be 1.

rest is easy………….

Answer 1

The correct option is (C)!

Sum $= x⊕y⊕z = x⊙y⊙z$
Carry $= zx + zy + xy$

When there are odd number of inputs then EXOR and EX-NOR gives the same truth table, as EXOR is an ODD function it means if there are odd number of 1's in the input then the output is 1, and EXNOR is an even function, it means if there are even number of 0's in the input then output will be 1.