How Do You Construct a Truth Table for a Digital Logic Circuit (AND; OR; NOT)?

A truth table lists every possible combination of binary inputs and shows the corresponding output of each logic gate. To construct one, list all input combinations, calculate intermediate outputs in circuit order, and then determine the final output.

Method

1. Identify the input variables, such as $A$ and $B$.
2. Create one column for each input. With $n$ inputs, there are $2^n$ possible input combinations.
3. Add columns for intermediate outputs and the final output.
4. Work through the circuit from inputs to output, one gate at a time.

The binary value $1$ represents true or a high signal, while $0$ represents false or a low signal.

Use a consistent counting pattern so no row is omitted: for two inputs, write $00$, $01$, $10$, and $11$. For three inputs, continue from $000$ to $111$, giving eight rows. The most significant input changes least often, while the least significant input alternates every row.

Worked Example

Suppose a circuit performs these operations:

• $X = \operatorname{NOT}(A)$
• $Z = X \operatorname{AND} B$
• $Y = Z \operatorname{OR} A$

There are two inputs, so the table needs $2^2 = 4$ rows.

The intermediate columns make the signal path visible. In the row $A=0$, $B=1$, NOT first changes $A$ to $X=1$; AND then gives $Z=$; OR finally gives . This order matters because each later gate uses the output produced by the preceding gate, not the original input.

A common misconception is that OR means “one input only.” Standard OR is inclusive: its output is also $1$ when both inputs are $1$.

IB Exam Technique

For B3.4 electronic systems, show every input combination and include intermediate columns for multi-gate circuits. Examiners reward systematic tracing; calculating only the final column increases the risk of carrying an unnoticed gate error through the table.