A 4bit synchronous counter uses flip-flops with a propagation delay time of 25ns each. The maximum possible time required for change of state will be
25 ns
Synchronous Counter State Change Time Analysis
This question asks about the time it takes for a 4-bit synchronous counter to change its state, considering the propagation delay of the flip-flops used.
Understanding Synchronous Counters
In a synchronous counter, all flip-flops change their state simultaneously during the active edge of the clock pulse. This means the clock signal is fed to all flip-flops at the same time.
Propagation Delay Explained
The propagation delay (often denoted as $t_{pd}$) of a flip-flop is the time interval between the application of a clock edge and the point at which the output of the flip-flop becomes stable and valid. Each flip-flop in this 4-bit counter has a propagation delay of 25ns.
Analyzing the State Change Timing
When a clock pulse arrives in a synchronous counter:
- All flip-flops receive the clock signal at virtually the same instant.
- Each flip-flop takes a certain amount of time (its propagation delay) to transition from its current state to the next state based on its inputs.
- The counter's overall state change is considered complete only when the outputs of *all* flip-flops have settled to their new, stable values.
- Therefore, the maximum time required for the entire counter to complete its state change is determined by the flip-flop with the longest propagation delay.
Calculation for the 4-bit Counter
Given:
- Number of bits = 4
- Propagation delay for each flip-flop ($t_{pd}$) = 25 ns
Since all flip-flops are triggered simultaneously by the clock and have the same propagation delay:
Maximum time for state change = Maximum propagation delay among all flip-flops
Maximum time = Maximum ($t_{pd\_FF1}$, $t_{pd\_FF2}$, $t_{pd\_FF3}$, $t_{pd\_FF4}$)
Maximum time = Maximum (25 ns, 25 ns, 25 ns, 25 ns)
Maximum time = 25 ns
Conclusion
The maximum time required for the state change in this 4-bit synchronous counter is dictated solely by the propagation delay of a single flip-flop, as they all operate in parallel triggered by the same clock edge. Thus, the time is 25 ns.
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