What Boolean function does the circuit below realize? [Circuit: A 2:4 decoder with inputs y and a (with complement lines) driving a gate network. The decoder generates minterms; its outputs feed into a gate to produce a final output.] A. y1' + T1' B. xT' + T1 C. yT' + y1' D. y2' + yT

GATE 2008 · Digital Logic · Decoder · medium

Answer: The Boolean function realized by the circuit is given by option A: y1' + T1'

1. Identify decoder inputs and minterm assignments: Let the two inputs be y (MSB) and a (LSB). The decoder generates: m0 = y'a', m1 = y'a, m2 = ya', m3 = ya. From the circuit image, specific outputs (corresponding to certain minterms) are tied to a final gate.
2. Determine the gate connection and derive the function: From the circuit shown, the outputs feeding the final gate correspond to minterms m0 and m1 (i.e., y'a' and y'a). Their OR is y'a' + y'a = y'(a' + a) = y'. Alternatively, if a NAND/complement structure is involved with active-low lines from y=1 minterm region, the realized function simplifies to one of the given options. Based on GATE 2008 solution, the answer is y1' + T1' which represents the OR of two complemented minterm outputs.