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How many flip-flops are required to produce a divide-by-16 device?a.2b.3c.8d.4

Question

How many flip-flops are required to produce a divide-by-16 device?a.2b.3c.8d.4

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Solution

The answer is d. 4.

Here's why:

A flip-flop is a circuit that can hold a binary digit, either a 0 or a 1. It's the simplest form of a sequential circuit, which means it changes state based on a sequence of inputs.

A divide-by-N device is a counter that sequences through N states for every cycle of input. In this case, we're looking for a divide-by-16 device, which means it needs to sequence through 16 states.

In binary, 16 is represented as 10000. This is a 5-bit number, but since we start counting from 0, we only need 4 bits to represent numbers up to 15 (which is 1111 in binary).

Therefore, we need 4 flip-flops to produce a divide-by-16 device. Each flip-flop holds one bit, so four flip-flops can hold a 4-bit number, which is enough to sequence through 16 states.

This problem has been solved

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