The 7420 IC is composed of two independent Four-Input NAND gates.

The truth table for the 4-input of the NAND is identical to that of the 2-Input variant. Naming the logical inputs and outputs as zeros and ones allows for easy calculation of the function performed.

Let inputs be marked as A, B, C, and D. The output will be called X.

Then, A * B * C * D = X Inverted. For example, if 2 of the inputs were logical one and two of them were logical zero, then 0*0*1*1 = 0, and the inverted state of 0 would equal 1, so the output of the gate would be one.

By a simpler method, simply consider the fact that the gate will only be output logical zero if and only if ALL inputs are logical one (HIGH).