GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 60

Question

The logic circuit above is used to compare two unsigned 2-bit numbers, $X_1 X_0=X$ and $Y_1 Y_0=Y$, where $X_0$ and $Y_0$ are the least significant bits. (A small circle on any line in a logic diagram indicates logical NOT.) Which of the following always makes the output $Z$ have the value 1?

• A. $X\gt Y$
• B. $X\lt Y$
• C. $X=Y$
• D. $X \neq Y$

Comments

Someone solve this question.

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Notice x1 and y1 are MSB's of the given 2 bit unsigned binary digits X and Y. So if x1>y1 then X>Y and we don't need to check LSB's. This is accomplished by the AND gate in the top left. If x1=1 and y1=0 (which means X>Y) it will output 1 and the final OR gate will output 1 (If x1=0 AND gate will produce output as 0 irrespective of what y1 is). Now if MSB's are equal, the middle XNOR gate will output 1. The AND gate in the top right checks the two LSB's. If x0=1 and y0=0 (meaning  X > Y since MSB's are equal) it will output 1, this will combine with XNOR output (which was 1) and will give 1 as output at final OR gate. Hence output is 1 only when X>Y.