Writing exam answers about Boolean logic

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Quick Questions

Shade in the A or B circle for each question.

1. Which logic expression is written the way a full-mark exam answer should be?

A X = (A AND B) OR C

B x = a and b or c

2. A question gives a circuit with inputs A, B, C and one output. How should you label it in your answer?

A Label every input A, B, C and the output X

B Label only the output and leave the inputs blank

3. A truth table for three inputs is asked for. How many rows must you complete?

A All 8 rows

B Only the rows where X is 1

4. The circuit has a gate whose output feeds another gate. What helps you show your working in the truth table?

A Skip the middle step and only write the final X column

B Add an extra working column for the middle gate's output

5. The exam gives you a problem statement and asks for a logic circuit. Which route is best?

A Guess the gates and draw them without any expression

B Write the expression from the statement, then draw the gates from it

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
1X = (A AND B) OR C		AX = NOT (A OR B)
2A B C \| A AND B \| X		BA truth table header with a working column, so the intermediate result is shown before the final output X.
3Label every input and the output so the examiner can follow your answer.		CThe truth table is incomplete because a row is missing. Two inputs need all 4 rows.
4A three-input truth table must be complete, with every one of the 8 rows filled in.		DGate names are not in capitals and there are no brackets, so the order of the gates is unclear.
5X = A and B or C		E2 x 2 x 2 = 8 rows
6A B \| X (only 3 of the 4 rows shown)		FA full-mark expression: output X is labelled, gate names are in capitals and brackets show that A AND B is worked out first.

Definitions

X = (A AND B) OR C

Fill in the Blanks

Complete each line of code by filling in the missing parts.

X = (A AND B) __ C

_ = (A AND B) OR C

3 inputs: 2 x 2 x 2 = _ rows

A B C | A AND B | X 0 1 1 | _ | 1

Problem: X is 1 only if A and B are both 1 X = A ___ B

Spot the Error

Shade in the letter of the line that contains an error.

Question 1

A X = A AND B OR C

B A B C | A AND B | X

C 0 0 0 | 0 | 0

D 0 0 1 | 0 | 1

Question 2

A Inputs: A, B

B Output: X

C X = not (A OR B)

Question 3

A A B | X = A AND B

B 0 0 | 0

C 0 1 | 1

D 1 0 | 0

E 1 1 | 1

Question 4

A Inputs: P, Q, R

B Output: X

C X = (A OR B) AND C

Question 5

A X = (A OR B) AND C

B A B C | A OR B | X

C 0 0 1 | 0 | 0

D 1 0 1 | 0 | 1

E 1 1 0 | 1 | 0

Answer Key

Writing exam answers about Boolean logic

Section A: Quick Questions

A — X = (A AND B) OR C

A — Label every input A, B, C and the output X

A — All 8 rows

B — Add an extra working column for the middle gate's output

B — Write the expression from the statement, then draw the gates from it

Section B: Match the Pairs

X = (A AND B) OR C → A full-mark expression: output X is labelled, gate names are in capitals and brackets show that A AND B is worked out first.

A B C | A AND B | X → A truth table header with a working column, so the intermediate result is shown before the final output X.

Label every input and the output so the examiner can follow your answer. → X = NOT (A OR B)

A three-input truth table must be complete, with every one of the 8 rows filled in. → 2 x 2 x 2 = 8 rows

X = A and B or C → Gate names are not in capitals and there are no brackets, so the order of the gates is unclear.

A B | X (only 3 of the 4 rows shown) → The truth table is incomplete because a row is missing. Two inputs need all 4 rows.

Section C: Definitions

X = (A AND B) OR C — A full-mark answer uses capital gate names, labelled inputs A, B, C and output X, correct brackets and a complete truth table with every row filled.

Section D: Fill in the Blanks

X = (A AND B) OR C

3 inputs: 2 x 2 x 2 = 8 rows

A B C | A AND B | X
0 1 1 | 0 | 1

Problem: X is 1 only if A and B are both 1
X = A AND B

Section E: Spot the Error

A — The brackets are missing. A full-mark expression must show the grouping, so line 1 should be X = (A AND B) OR C.

C — Gate names must be written in capital letters. The expression should be X = NOT (A OR B).

C — AND only outputs 1 when both inputs are 1. With A = 0 and B = 1 the output X must be 0, so the row should be 0 1 | 0.

A — Exam questions use the input labels A, B and C. The expression uses A, B and C, so line 1 should be Inputs: A, B, C.

D — The working column is wrong. When A = 1 and B = 0, A OR B is 1, not 0. The row should be 1 0 1 | 1 | 1.