Combining gates

Martin McBride, 2017-01-16
Tags or gate and gate truth table
Categories logic logic gates

We can combine two or more gates to perform more complex functions.

Combining gates

In this diagram, we have three inputs (A, B and C) and one output (Q). We are using an AND gate and an OR gate.


We have also labelled the output of the AND gate as D. D is not an input, it is an intermediate value which we will use when calculating the truth table.

Truth table

Since this circuit has 3 inputs, the truth table will have 8 rows. Here is the basic truth table, with space for D and Q to be added:


D is equal to A AND B, so we can easily fill out the D column in the table. We just put 1 everywhere that A and B are both 1, and 0 everywhere else. Notice that D doesn't depend on C in any way:


Q is equal to D OR C, so we can now fill out the Q column in the table - the actual output of the combination gate. We just put 1 everywhere that either D or C are 1, and 0 everywhere else:


Interactive example

Here is an interactive combined gate. Click on the inputs A, B and C to change their state, and see the output value Q.


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