Question

A synchronous 3-bit binary counter is currently in state \(\text{Q}_2\text{Q}_1\text{Q}_0=101\). After two clock pulses, its state will be

• A. \(111 \)
• B. \(000 \)
• C. \(001 \)
• D. \(010 \)

Hint:

Unless a question specifies that a counter is a "down-counter" or lists explicit non-standard state logic equations, always assume a counter counts upward sequentially in binary. Just convert to decimal, add the clock pulses, and convert back: \[ 5 + 2 = 7 \rightarrow 111 \] This takes just a few seconds on a test!

Answer 1

The Correct Option is A

Concept: A standard 3-bit binary counter tracks numbers sequentially in upward binary order from $000$ to $111$ (which corresponds to decimal values from 0 to 7). The term "synchronous" implies that all flip-flops share a common clock line and transition simultaneously, preventing intermediate transient glitches, but the overall state sequence still tracks standard binary counting progression unless specified otherwise. The sequence repeats every $2^3 = 8$ clock states: \[ 000_2 (0) \rightarrow 001_2 (1) \rightarrow 010_2 (2) \rightarrow 011_2 (3) \rightarrow 100_2 (4) \rightarrow 101_2 (5) \rightarrow 110_2 (6) \rightarrow 111_2 (7) \rightarrow 000_2 (0) \]

Step 1: Identifying the initial decimal state value.
The given initial state configuration is: \[ Q_2 Q_1 Q_0 = 101_2 \] Let's convert this binary combination into its equivalent base-10 integer representation: \[ \text{Decimal Value} = (1 \times 2^2) + (0 \times 2^1) + (1 \times 2^0) = 4 + 0 + 1 = 5 \]

Step 2: Adding the two clock pulses sequentially.
Since it is a standard up-counter, each active clock pulse increments the internal state value by exactly one:
• Initial State: \(5 \quad (101_2)\)
• After 1st Clock Pulse: \(5 + 1 = 6 \quad \rightarrow \quad 110_2\)
• After 2nd Clock Pulse: \(6 + 1 = 7 \quad \rightarrow \quad 111_2\)

Step 3: Re-writing the final state back in binary layout.
The decimal value 7 written as a 3-bit binary code is: \[ Q_2 Q_1 Q_0 = 111_2 \] Hence, the correct choice is option (1).