5. Logic Gates

Question.8

A 2-bit comparator checks whether two binary values A1A0 and B1B0 are identical.

The circuit should work as:

X1 = A1 XNOR B1
X0 = A0 XNOR B0
MATCH = X1 · X0

During testing, the following outputs are observed:

`A1A0`	`B1B0`	Expected `MATCH`	Observed `MATCH`
10	10	1	1
10	11	0	1
10	00	0	1
10	01	0	0

Both XNOR gates are confirmed to be working correctly.

Which gate is most likely used incorrectly at the final stage?

Need Help? Refer to the Quick Guide below

Logic gates are the basic building blocks of digital circuits. They receive one or more binary inputs and generate a binary output.

Binary values:

In positive logic:

Basic Logic Gates

An AND gate produces 1 only when all inputs are 1.

An OR gate produces 1 when at least one input is 1.

A NOT gate produces the complement of its input. It is also called an inverter.

NAND and NOR are universal gates. Either NAND gates alone or NOR gates alone can implement any Boolean function.

A NAND gate is an AND gate followed by a NOT operation.

A NOR gate is an OR gate followed by a NOT operation.

A two-input XOR gate produces 1 when its inputs are different.

Common uses:

A two-input XNOR gate produces 1 when its inputs are equal.

Common uses:

Universal gates recreate AND, OR, and NOT by using tied inputs or by adding an inversion stage.

AND, OR, NAND, and NOR gates commonly have multiple inputs.
Multi-input XOR produces 1 when the number of HIGH inputs is odd, while multi-input XNOR produces 1 when the number of HIGH inputs is even.
A NOT gate always has one input.

Logic gates are used in:

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