4-Bit Synchronous Up/Down Counter: T Expression Derivation
Timers, PWM generators, and motor controllers rely on up/down counters to track bidirectional movement or time. The toggle condition for each bit in a synchronous counter depends on the count direction: up-counting looks for a chain of ones, while down-counting looks for a chain of zeros.
Derive and implement the combinational logic for the T-flip-flop input T1 of the second stage (bit 1) in a 4-bit synchronous up/down counter. The circuit evaluates the current state of the first bit Q0 and the mode control signals UP and DOWN to determine if the second bit should toggle.
| UP | DOWN | Q0 | T1 | |------|--------|------|------| | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 0 | | 0 | 1 | 0 | 1 | | 0 | 1 | 1 | 0 | | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 1 |
Assume the system guarantees UP and DOWN are never asserted simultaneously.
Constraints
- Use only combinational logic gates.
- Do not use sequential elements, multiplexers, or arithmetic blocks.
Topics
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