Truth Table Workshop

Logic in a table

Deep inside every computer, tiny logic gates make decisions using just two values: 1 for true and 0 for false. The gates combine inputs with the operators AND, OR and NOT. A truth table lays out the output for every possible combination of inputs, so you can see exactly what a logic circuit does.

The logic operators

Four ideas run through this module:

AND and OR

The two operators that combine two inputs are AND and OR. Both take inputs of 1 for true or 0 for false.

Match each operator

Fill the AND table

AND outputs 1 only when both inputs are 1. Work out the output column, and pick each value from 0 and 1.

Read the OR table

In an OR truth table, what is the output when A = 0 and B = 1?

• 1
• 0
• 2
• Both 0 and 1

Logic in words

A truth table lists the output for every possible _____ of inputs. The AND operator gives 1 only when _____ inputs are 1. The OR operator gives 1 when at _____ one input is 1. The NOT operator _____ its input. To be systematic, list the rows in _____ order.

Working systematically

With two inputs there are four rows; with three inputs there are eight. To be sure you list them all, use binary-count order: 00, 01, 10, 11 for two inputs, and 000 up to 111 for three. For a combined expression like (A AND B) OR C, add an intermediate column for A AND B first, then work out the final column from it.

Count in binary

Put these two-input rows into binary-count order, from lowest to highest.

• A = 0, B = 0
• A = 0, B = 1
• A = 1, B = 0
• A = 1, B = 1

Fill the combined table

Here A AND B is already worked out. Fill the final column, (A AND B) OR C, which is 1 whenever A AND B is 1 or C is 1.

Read the NOT gate

The NOT operator inverts its input. What is the output of NOT 1?

• 0
• 1
• 2
• It stays the same

What each gate does

Tap the TWO statements that are TRUE about truth tables and logic.

• AND outputs 1 only when both of its inputs are 1.
• OR outputs 1 only when both inputs are 1.
• A truth table for three inputs has eight rows.
• NOT leaves its input unchanged.
• A logic output can be any whole number.

Build the expression

Work out (A OR B) AND NOT C step by step, for the inputs A = 1, B = 0 and C = 1.

• First, what is A OR B when A = 1 and B = 0?
• Next, what is NOT C when C = 1?
• Finally, what is (A OR B) AND NOT C, which is 1 AND 0?

Build a truth table

Explain how to construct a truth table for a three-input expression such as (A AND B) OR C. Write in clear, full sentences.

• Explain how many rows the table needs and how to order them
• Explain what an intermediate column is and why it helps
• Work out the value in the A AND B column for the row A = 1, B = 1, C = 0
• Give the final output for that same row