Boolean algebra practice · A-Level Computer Science 9618

Original questions All questions on this page are original work, written in the Cambridge AS & A Level style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

How to earn the marks

Show every law.

Notation: A.B is AND, A + B is OR, a bar is NOT; keep bars clearly over the right letters.
De Morgan: break the bar and change the operator, one bracket at a time.
Look for patterns: X + X.Y = X, X + NOT X.Y = X + Y, X + NOT X = 1, X.NOT X = 0.
Check: compare a few rows of the truth table of your answer with the original.

Recall

[2 marks]

State De Morgan's laws for two inputs, A and B.

A.B = A + B ✓
A + B = A.B ✓

Apply

[3 marks]

Simplify X = A.B + A.B + A.B. Show your working.

= A.(B + B) + A.B (distributive: take out NOT A) ✓
= A + A.B (inverse and identity) ✓
= A + B (redundancy: NOT A + A.B = NOT A + B) ✓

Apply

[2 marks]

Use De Morgan's laws to write A.B.C without a bar over the whole expression, then simplify it.

A.B.C = A + B + C (De Morgan for three inputs) ✓
= A + B + C (double complement) ✓

Apply

[3 marks]

Show that (A + B).A.B = A.B + A.B.

= (A + B).(A + B) (De Morgan) ✓
= A.A + A.B + B.A + B.B (distributive: multiply out) ✓
= A.B + A.B (inverse: A.NOT A = 0 and B.NOT B = 0, then commutative) ✓
This is A XOR B. ✓

Apply

[4 marks]

Simplify X = A.B.C + A.B.C + A.B.C. Show your working.

= A.B.(C + C) + A.B.C (distributive: take out A.B) ✓
= A.B + A.B.C (inverse and identity) ✓
= A.(B + B.C) (distributive: take out A) ✓
= A.(B + C) (redundancy: B + NOT B.C = B + C) ✓
= A.B + A.C (either form earns the mark) ✓

Analysis

[3 marks]

A student writes: A + B = A + B. Show that the student is wrong and give the correct expression.

Take A = 1, B = 0: A + B = 1 = 0. ✓
But A + B = 0 + 1 = 1, so the two expressions are not equal. ✓
The student broke the bar but did not change the operator: the correct expression is A.B. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.