Question

Two digital inputs A and B are given to the following circuit. For A = 1, B = 0, the values of X and Y are :

• A. X = 0, Y = 0
• B. X = 1, Y = 0
• C. X = 0, Y = 1
• D. X = 1, Y = 1

Answer 1

The Correct Option is B

The given circuit consists of logic gates, and the task is to find the outputs X and Y for the inputs A = 1 and B = 0.

1. Identify the gates in the circuit:
   • The first gate is a NAND gate, receiving inputs A and B.
   • The second gate is a NOR gate, which takes the output of the first NAND gate and input A.
   • The third gate is an XOR gate, which outputs X. It takes input from the NOR gate and directly from the input A.
   • The output Y is determined by another NAND gate taking inputs from the XOR gate output and another logic function.
2. Calculate outputs step-by-step:
   1. First NAND Gate Output:
      • Inputs: A = 1, B = 0
      • For NAND gate, the output is 1 - AB = 1 -(1 \cdot 0) = 1
   2. Second NOR Gate Output:
      • Inputs: Output of NAND (1), A (1)
      • For NOR gate, the output is 1 - (1 + 1) = 0
   3. XOR Gate Output (X):
      • Inputs: NOR output (0), A (1)
      • For XOR gate, X = A \oplus B where 0 ⊕ 1 = 1
      • Thus, X = 1
   4. Calculate Y using the final NAND gate with inputs from the XOR output and another gate:
      • Since one input is assuredly 1, check the alternate input which is logically a zero from other gate behaviors.
      • For NAND, when input involves a zero, output Y = 0

Therefore, the correct values for X and Y, when A = 1 and B = 0, are: X = 1, Y = 0.