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Combinational and Sequential Circuits

GATE CSE 2014 Set 2 · Q7

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Let k=2nk = 2^n. A circuit is built by giving the output of an nn-bit binary counter as input to an nn-to-2n2^n bit decoder. This circuit is equivalent to a

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Solution

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Official answer: C) k-bit ring counter.

Combinational and Sequential Circuits

An nn-bit binary counter has 2n=k2^n = k distinct states (0,1,…,k−1)(0, 1, \dots, k-1).

An nn-to-2n2^n decoder takes nn inputs and activates exactly one of its 2n=k2^n = k output lines corresponding to the binary value of the input.

As the nn-bit binary counter cycles through all its kk counts, the decoder activates output line 00, then line 11, …\dots, up to line k−1k-1, and then wraps around to line 00. At any point in time, exactly one of the kk lines is active (HIGH), and this active state rotates sequentially across all kk outputs.

This behavior matches a kk-bit ring counter, which consists of kk flip-flops with a single circulating active bit (1).

Therefore, (C) is the correct option.

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This Combinational and Sequential Circuits previous year question is Q7 of the GATE CSE 2014 Set 2 paper. Find more GATE CSE PYQs on Combinational and Sequential Circuits in Digital Logic, or browse all GATE CSE PYQs.

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Combinational and Sequential Circuits in GATE CSE

Combinational and Sequential Circuits has 32 GATE CSE PYQs across 22 papers from 2011 to 2026. 8 of them are 1-mark MCQs like this one, and it is the only one in GATE CSE 2014 Set 2.

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GateAI solution cardGATE CSE 2014 Set 2 · Q7 · MCQ

Let k = 2n. A circuit is built by giving the output of an n-bit binary counter as input to an n-to-2n bit decoder. This circuit is equivalent to a

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.