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Show that an n-bit binary counter connected to an n− to- 2* line decoder is equivalent to a ring counter with 2* flip-flops. Draw the block diagram of both circuits for n=3. How many timing signals are generated?

User Ken Sharp
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Final answer:

An n-bit binary counter connected to an n-to-2* line decoder is equivalent to a ring counter with 2* flip-flops. The binary counter counts in binary from 0 to 2**n-1, while the ring counter creates a cyclic sequence of states. For n=3, the binary counter has 3 flip-flops and the ring counter has 4 flip-flops. The number of timing signals generated is equal to the number of flip-flops in each circuit.

Step-by-step explanation:

To show that an n-bit binary counter connected to an n-to-2* line decoder is equivalent to a ring counter with 2* flip-flops, we need to understand the basic operations of both circuits. An n-bit binary counter is a sequential circuit that counts in binary from 0 to 2**n-1. Each flip-flop represents a bit, and the outputs of the flip-flops are connected to the inputs of the decoder. The decoder converts the binary count to its corresponding output state. In a ring counter, each flip-flop represents a bit, and the outputs of the flip-flops are connected in a loop, with one flip-flop's output connected to the next flip-flop's input. This creates a cyclic sequence of states.

In the case of n=3, the block diagram of the binary counter with a 3-to-8 line decoder would have 3 flip-flops and 8 output lines, with each output line representing a different state. The block diagram of the ring counter with 4 flip-flops would have 4 flip-flops connected in a loop, where the output of one flip-flop is connected to the input of the next flip-flop. Each flip-flop represents a different state.

The number of timing signals generated in both circuits is equal to the number of flip-flops in the circuit. In the case of the binary counter, there are 3 flip-flops, so 3 timing signals are generated. In the case of the ring counter, there are 4 flip-flops, so 4 timing signals are generated.

User Vinnitu
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