← IGCSE Computer Science Paper 2

Intermediate columns in a truth table

An extra truth table column for a bracket or gate output, such as P = A AND B. It is filled in first, so the final output X can be worked out step by step from earlier columns.

Part of: IGCSE Computer Science 0478 — 10 Boolean Logic — Module 22

Understanding Intermediate columns in a truth table in IGCSE Computer Science Paper 2

What it does: The expression X = (A AND B) OR C is split into P for the bracket and a final step that uses the earlier column P. The bracket (A AND B) is worked out first, so it gets its own column P. Then X = P OR C. Intermediate columns do not change the inputs. They break a multi-gate expression into small steps. NOT reverses the input. NOT 1 gives 0, so Q = 0 in every row where A = 1. P = A AND B must be filled in first. X then uses P and C. AND outputs 1 only when both inputs are 1. Here A and B are both 1, so P = 1.

Common mistakes: The bracket in the expression is (A AND B), so intermediate column P must be A AND B, not A OR B. The expression must match the columns below it. Columns P and Q are combined with AND, so the expression should be X = (A OR B) AND NOT C.

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This module's key terms are also in a printable crossword (Modules 552–561) and word search (Modules 539–580).

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Learning

Duo

For X = (A AND B) OR C, which extra column would you fill in first?

P = A OR CP = A AND B

Matches

Row A=1, B=0: P = A AND B = 1

↓

P is worked out wrongly. 1 AND 0 gives 0, because AND needs both inputs to be 1. The wrong value in P then spoils the final output X.

Applying

Meanings

Term

intermediate column

Meaning

An extra truth table column for a bracket or gate output, such as P = A AND B. It is filled in first, so the final output X can be worked out step by step from earlier columns.

Practice

P = A AND B

Testing

Gaps

P = A B

Check Answer

Spots

1X = (A AND B) OR NOT A

2P = A OR B

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Quick Questions

1. For X = (A AND B) OR C, which extra column would you fill in first?

A. P = A AND B ✓

B. P = A OR C

The bracket (A AND B) is worked out first, so it gets its own column P. Then X = P OR C.

2. Why add an intermediate column to a truth table?

A. To work out one gate or bracket at a time ✓

B. To add an extra input to the circuit

Intermediate columns do not change the inputs. They break a multi-gate expression into small steps.

3. For X = (NOT A) AND B, a column Q holds NOT A. What is Q when A = 1?

A. Q = 0 ✓

B. Q = 1

NOT reverses the input. NOT 1 gives 0, so Q = 0 in every row where A = 1.

4. Which column is filled in last for X = (A AND B) OR C?

A. The intermediate column P

B. The final output column X ✓

P = A AND B must be filled in first. X then uses P and C.

5. In the row A = 1, B = 1, what is P if P = A AND B?

A. P = 0

B. P = 1 ✓

AND outputs 1 only when both inputs are 1. Here A and B are both 1, so P = 1.

Match the Pairs

P = A AND B → An intermediate column that holds the output of the bracket (A AND B) for every row, before the final output X is worked out

Q = NOT A → An intermediate column that holds the opposite of input A in each row, ready to be used in a later column

Work out the bracket first in its own column P, then use P with C to find the final output X → P = A AND B, X = P OR C

Give the NOT A result its own column Q, then combine Q with the P column in the last column → X = Q AND P

Row A=1, B=0: P = A AND B = 1 → P is worked out wrongly. 1 AND 0 gives 0, because AND needs both inputs to be 1. The wrong value in P then spoils the final output X.

Final column X = (A AND B) OR C, filled in before column P → The intermediate column P should be completed first. X uses P, so filling in X before P makes the step by step method impossible and invites errors.

Key Term

intermediate column

An extra truth table column for a bracket or gate output, such as P = A AND B. It is filled in first, so the final output X can be worked out step by step from earlier columns.

Fill in the Blanks

1. X = (A AND B) OR C P = A AND B

Hint: Type the gate that the bracket in the expression uses to make column P.

2. X = (NOT A) AND B Q = NOT A

Hint: Type the gate that fills column Q, which holds the bracket's result.

3. X = (A AND B) OR (NOT A) P = A AND B, Q = NOT A X = P OR Q

Hint: Type the gate that joins the two earlier columns, as in the full expression on line 1.

4. X = (A AND B) OR C P = A AND B X = P OR C

Hint: Type the name given to the extra column that holds the bracket output.

5. P = A AND B Q = NOT A X = P OR Q

Hint: Type the name of the earlier column that holds the result of A AND B.

Spot the Error

Question 1

A X = (A AND B) OR NOT A

B P = A OR B

C Q = NOT A

D X = P OR Q

Line B — The bracket in the expression is (A AND B), so intermediate column P must be A AND B, not A OR B.

Question 2

A X = (A OR B) OR NOT C

B P = A OR B

C Q = NOT C

D X = P AND Q

Line A — The expression must match the columns below it. Columns P and Q are combined with AND, so the expression should be X = (A OR B) AND NOT C.

Question 3

A X = NOT A AND (B OR C)

B P = NOT A

C Q = B OR C

D X = P OR Q

Line D — The expression joins NOT A and (B OR C) with AND, so the final column must be X = P AND Q.

Question 4

A A = 1, B = 0

B P = A AND B = 0

C Q = NOT A = 1

D X = P OR Q = 0

Line C — When A is 1, NOT A is 0, so the value in column Q is 0. The line should be Q = NOT A = 0.

Question 5

A X = (NOT A) OR B

B P = NOT B

C X = P OR B

Line B — Column P holds the first part of the expression, which is NOT A. It should be P = NOT A, not NOT B.

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