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Which logic gates should be used to create a circuit that outputs a 1 when the number of 1s on inputs a, b, c, d is odd?

a) XOR gates only
b) OR gates only
c) AND gates only
d) NOR gates only

1 Answer

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Final answer:

To achieve an output of 1 for an odd number of 1s on inputs, XOR gates should be used. The arrangement involves using three XOR gates where inputs a, b form one pair and c, d form another; their outputs are then combined via a third XOR gate to give the final result.

Step-by-step explanation:

To create a circuit that outputs a 1 when the number of 1s on inputs a, b, c, d is odd, you should use XOR gates only. The XOR (Exclusive OR) gate is a digital logic gate that gives a true (1) output when the number of true inputs is odd.

For a set of four inputs like a, b, c, and d, you can connect them using XOR gates in a specific arrangement to ensure that if there is an odd number of 1s, the output will be 1.

You would start by connecting inputs a and b to an XOR gate, and c and d to another XOR gate. Then, take the output of these two XOR gates and connect them to a third XOR gate.

The final output of this third XOR gate will be 1 if the number of 1s among the inputs a, b, c, and d is odd, and 0 if it is even.

OR gates should be used to create a circuit that outputs a 1 when the number of 1s on inputs a, b, c, d is odd. An OR gate outputs a 1 if any of its inputs are 1.

By connecting all the inputs to the OR gate, any occurrence of 1 will result in an output of 1. The odd number of 1s will ensure that the output is 1.

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