Question

amt general comp 11: question 26 of 60
which of the following logic gates will provide an active high out only when all inputs are different?
a xnor.
b nand.
c xor.

Explanation:

• XNOR (Option A): Outputs high when all inputs are the same.
• NAND (Option B): Outputs low when all inputs are high.
• XOR (Option C): For two - input XOR, output is high when inputs are different. For more than two inputs, the output is high when the number of high inputs is odd. When all inputs are different (in a multi - input case, if we consider binary inputs, for example, with three inputs \(A\), \(B\), \(C\) where \(A = 0\), \(B=1\), \(C = 0\) (not all different) vs \(A = 0\), \(B = 1\), \(C=1\) (not all different) vs \(A=0\), \(B = 1\), \(C\) is considered in a way that for a general multi - input XOR (constructed as a cascade of two - input XORs), the output is high when there is an odd number of high inputs. When all inputs are different (in a binary - input - based multi - input scenario, we can think of it in terms of the XOR operation's property of being \(1\) when the input combination has an odd number of \(1\)s. If we assume two distinct binary values for inputs, having all inputs different in a multi - input (even number of inputs case is not possible as we have only two binary values \(0\) and \(1\), for odd number of inputs, we will have an odd number of non - equal (different in terms of binary values) inputs. For example, with three inputs, if they are different (in terms of binary values), we have two of one value and one of the other. The XOR of three variables \(A\oplus B\oplus C=(A\oplus B)\oplus C\). If \(A = 0\), \(B = 1\), \(C=0\), \((0\oplus1)\oplus0=1\oplus0 = 1\); if \(A = 0\), \(B = 1\), \(C = 1\), \((0\oplus1)\oplus1=1\oplus1 = 0\). But if we consider the general definition of XOR for multiple inputs (where the output is \(1\) when there is an odd number of \(1\)s among the inputs. When we say all inputs are different (in a binary - input multi - input gate, we can re - frame it as having an odd number of non - zero (high) inputs).

Answer:

C. XOR