Discussion
The binary output Y3 Y2 Y1 Y0 of the following logic circuit for the inputs X3 X2 X1 X0 = 1 0 1 1 is :
Answer: A
The output is 1 1 0 1.
The circuit is a Gray-to-binary converter: \(Y_{3} = X_{3}\), and each lower bit is the XOR of the next higher output bit with the corresponding input:
- \(Y_{3} = X_{3} = 1\)
- \(Y_{2} = Y_{3} \oplus X_{2} = 1 \oplus 0 = 1\)
- \(Y_{1} = Y_{2} \oplus X_{1} = 1 \oplus 1 = 0\)
- \(Y_{0} = Y_{1} \oplus X_{0} = 0 \oplus 1 = 1\)
Feeding each XOR with neighbouring input bits instead (binary-to-Gray) would give 1 1 1 0, which is not offered. 1 0 1 0 and 0 1 0 1 do not satisfy \(Y_{3} = X_{3} = 1\) together with the XOR chain.
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