Creating a logic circuit from a problem statement

Name:

Date:

Class:

Quick Questions

Shade in the A or B circle for each question.

1. Problem statement: an alarm X sounds when switch A and switch B are both on, or when switch C is on. Which expression matches?

A X = A AND (B OR C)

B X = (A AND B) OR C

2. What is the FIRST step when drawing a circuit from a problem statement?

A Write the logic expression

B Draw gates straight away and guess the wiring

3. How many gates are needed to draw X = (A AND B) OR C?

A 2 gates: one AND and one OR

B 3 gates: one for each input A, B and C

4. In the circuit for X = (A AND B) OR C, what goes into the OR gate?

A Inputs A and B directly, plus input C

B The output of the AND gate and input C

5. Should you simplify the expression before drawing the circuit?

A No, draw exactly what the expression says

B Yes, always simplify it first

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		AThe steps are in the wrong order and the brackets are missing. The expression must be written first from the problem statement, and the circuit drawn from it.
2X = NOT (A OR B) AND C		BDraw an AND gate for A and B, then feed its output and C into an OR gate whose output is X
3Problem statement: 'The alarm X sounds when switch A and switch B are both on, or when sensor C is on.' Write the expression first.		CThe expression has been simplified before drawing. The circuit must be drawn from the expression as written, without simplification.
4Problem statement: 'The motor X runs when sensor A is on and sensor B is not on.' Write the expression first.		DX = A AND (NOT B)
5Drawing the gates first, then writing X = A AND B OR C afterwards from the picture		EX = (A AND B) OR C
6X = A OR B simplified from X = (A AND B) OR (A AND NOT B)		FDraw an OR gate for A and B, put a NOT gate on its output, then feed that and C into an AND gate whose output is X

Definitions

X = (A AND B) OR C

Fill in the Blanks

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

Statement: X is 1 if A and B are 1, or C is 1 X = (A AND B) __ C

Motor X runs when A and B are both 1 _ = A AND B

Alarm X is on if A is on and B is off X = A AND ___ B

Step 1: write the logic __________ Step 2: draw one gate per operator

X = (A AND B) OR (A AND C) Gates to draw without simplifying: _

Spot the Error

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

Question 1

A Statement: A and B both on

B Expression: X = A AND B

C Draw: OR gate, inputs A, B

D Output of gate is labelled X

Question 2

A Statement: A or C is on

B Expression: X = A AND C

C Draw: OR gate, inputs A, C

D Output is labelled X

Question 3

A Statement: X on if A is off

B Expression: X = NOT A

C Draw: NOT gate, inputs A, B

Question 4

A Statement: A and B, or C

B Expression: X = (A AND B) OR C

C Gate 1: AND, inputs A and B

D Gate 2: OR, inputs A and C

E Output of gate 2 is X

Question 5

A Step 1: draw the gates first

B Step 2: gate for each operator

C Step 3: label inputs A, B, C

D Step 4: label the output X

Answer Key

Creating a logic circuit from a problem statement

Section A: Quick Questions

B — X = (A AND B) OR C

A — Write the logic expression

A — 2 gates: one AND and one OR

B — The output of the AND gate and input C

A — No, draw exactly what the expression says

Section B: Match the Pairs

X = (A AND B) OR C → Draw an AND gate for A and B, then feed its output and C into an OR gate whose output is X

X = NOT (A OR B) AND C → Draw an OR gate for A and B, put a NOT gate on its output, then feed that and C into an AND gate whose output is X

Problem statement: 'The alarm X sounds when switch A and switch B are both on, or when sensor C is on.' Write the expression first. → X = (A AND B) OR C

Problem statement: 'The motor X runs when sensor A is on and sensor B is not on.' Write the expression first. → X = A AND (NOT B)

Drawing the gates first, then writing X = A AND B OR C afterwards from the picture → The steps are in the wrong order and the brackets are missing. The expression must be written first from the problem statement, and the circuit drawn from it.

X = A OR B simplified from X = (A AND B) OR (A AND NOT B) → The expression has been simplified before drawing. The circuit must be drawn from the expression as written, without simplification.

Section C: Definitions

X = (A AND B) OR C — Turn the problem statement into a logic expression first, then draw one gate for each operator to build the circuit. Use inputs A, B, C (up to three) and one output X. Do not simplify.

Section D: Fill in the Blanks

Statement: X is 1 if A and B are 1, or C is 1
X = (A AND B) OR C

Motor X runs when A and B are both 1
X = A AND B

Alarm X is on if A is on and B is off
X = A AND NOT B

Step 1: write the logic expression
Step 2: draw one gate per operator

X = (A AND B) OR (A AND C)
Gates to draw without simplifying: 3

Section E: Spot the Error

C — The statement says A and B must both be on, so the expression uses AND. The gate drawn must be an AND gate, not an OR gate.

B — The statement says A or C, so the expression must use OR. It should be X = A OR C.

C — A NOT gate has exactly one input, and the statement only mentions A. It should be: NOT gate, input A.

D — The OR gate must take the output of gate 1 (A AND B) as one input, not A on its own. It should be inputs G1 and C.

A — The logic expression must be written first. The gates are then drawn from that expression, one for each operator.