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A two-bit binary counter is a digital circuit that counts in binary from 00 to 11, representing decimal values 0 to 3. It uses two flip-flops to store the two bits, where each flip-flop represents one bit of the counter. The counter increments by one with each clock pulse, cycling through the states 00, 01, 10, and 11. This type of counter can be used in various applications, such as in digital clocks and frequency dividers.

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