How propagation of ‘X’ happens through different logic gates

‘X’ refers to a signal attaining a value that is ‘unknown’. It can be either ‘0’ or ‘1’. But, the exact value of the signal is not known. If a simulator is not able to decide whether a logic value should be logic ‘0’ or logic ‘1’, it will assign a value ‘X’ to the value. An example of ‘X’ source is a logic block that has not been initialized properly through reset. Having an ‘X’ value at a node can propagate to the logic lying in the fan-out, thereby increasing the uncertainty downstream the logic.

How ‘X’ propagates: An ‘X’ value at the input of a logic gate may or may not propagate to its output depending upon the states at other inputs of the logic gate. Given below is how different logic gates react to ‘X’ values:

1)  OR gate: An OR gate can absorb an ‘X’ if the other input has logic ‘1’. Otherwise, ‘X’ propagates through it. Please refer figure 1 for explanation:

Figure 1: X-propagation through OR gate

2) AND gate: An AND gate can absorb ‘X’ if the other input has logic ‘0’. Otherwise, ‘X’ propagates through it. Please refer figure 2 for explanation:

Figure 2: X-propagation through AND gate

3) Buffer/inverter: Since, buffers/inverters are single input gates, an ‘X’ at the input means ‘X’ at the output.

4) XOR gate: An ‘X’ at one of the inputs of XOR produces ‘X’ at the output no matter what the 

other input state is. Please refer truth table given in Figure 3 for explanation:

Figure 3: X-propagation through XOR gate

5) Complex gates: For complex gates, whether ‘X’ will propagate to the output depends upon the overall function of the ‘X’ input with respect to other gates. E.g. suppose a gate with function

Z = A + (B * C)

Then, if B input goes ‘X’, the output will go ‘X’ if A=0 and C=1.

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