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Digital Logic - Truth Tables, Part II

We looked at truth tables previously:

A truth table is a list of each output resulting from each possible combination of inputs

Inputs:

Let's review how we fill a truth table for a given gate. To fill a truth table, we will look at every possible combination of inputs, put those inputs in the circuit, then find the resulting output. To guarantee that we cover every possible combination, we will order the rows of the truth table by counting in binary - for example, let's use 0 for FALSE and 1 for TRUE:

Count from 0 to 3 in binary:

00 -> FALSE FALSE
01 -> FALSE TRUE
10 -> TRUE FALSE
11 -> TRUE TRUE

... these will form the input columns in the truth table

If we have 3 inputs, we will have 8 rows (binary numbers 0 through 7)

000 > False False False
001 > False False True
010 > False True   False
011 > False True   True
100 > True   False False
101 > True   False True
110 > True   True   False
111 > True   True   True

For 4 inputs, use binary 0 through 15 (0000 through 1111).

Filling Truth Tables:

Once the input colums are set, apply each combination to the circuit and find the output. For example, the first row is filled:

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The rest of the table is filled:

The same process is used for more complex circuits also.

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