4-Bit Synchronous Binary Counter: Carry Chain Derivation
Program counters, timers, and frequency dividers rely on synchronized state transitions to maintain precise timing. A synchronous binary counter updates all bits simultaneously by sharing a common clock edge, requiring combinational logic to determine when each bit should toggle.
Implement a 4-bit synchronous up-counter using T flip-flops. The outputs Q3, Q2, Q1, and Q0 represent the 4-bit binary value, where Q0 is the least significant bit. The counter must increment by one on every active high edge of clk. A reset signal rst forces all outputs to 0 asynchronously. Derive the toggle expressions T3, T2, T1, and T0 for each bit based on the current state of the lower-order bits.
| Q3 | Q2 | Q1 | Q0 | T3 | T2 | T1 | T0 | |------|------|------|------|------|------|------|------| | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Constraints
- Use exactly four T-type flip-flops.
- Connect all flip-flop clock pins to the single
clkinput. - Derive the toggle inputs
T0,T1,T2, andT3using only AND gates. - Connect
rstto the asynchronous reset pin of every flip-flop.
Topics
Solve this problem
Place the gates, wire them up and watch the signals settle. Every submission runs on the same simulation engine that grades it.
This problem is part of Codiode Pro. The statement above is free to read.
The circuit builder and code editor need a desktop screen. On a phone, read the problem here and open it on a laptop to solve.