Creating a logic circuit from an expression

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Quick Questions

Shade in the A or B circle for each question.

1. To draw a circuit for X = (A AND B) OR C, which gate do you draw first?

A The AND gate, because it is in the brackets

B The OR gate, because it gives the final output X

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

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

B 2 gates: one AND and one OR

3. In X = (A AND B) OR C, where does input C connect?

A To the AND gate along with A and B

B Directly to the OR gate

4. For X = (A OR B) AND C, which gate produces the final output X?

A The AND gate

B The OR gate

5. How do you draw X = NOT A for a circuit?

A One NOT gate with A as its only input

B One NOT gate with A and a second input of 0

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 gates are swapped. The bracket contains AND, so A and B go into an AND gate first, and the OR gate comes last with C.
2X = NOT (A OR B)		BDraw an AND gate for A and B first, then feed its output and C into a final OR gate that gives X
3Draw one gate for each operator, so an expression with two operators needs two gates joined by a wire		CDraw an OR gate for A and B, then pass its output through a NOT gate to give X
4A NOT applied to a single input is drawn as a NOT gate on that input before it reaches the next gate		DThe OR in the bracket was left out. Every operator needs its own gate, so A and B must go into an OR gate whose output feeds the AND gate with C.
5For X = (A AND B) OR C, drawing an OR gate for A and B, then an AND gate with C		EX = (A OR B) AND C
6For X = (A OR B) AND C, drawing one AND gate with the inputs A, B and C and no OR gate		FX = (NOT A) AND B

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) OR C Gate 1 (bracket): ___ gate, inputs A and B Gate 2: OR gate, inputs Gate 1 and C

X = (A OR B) AND C Gate 1: OR gate, inputs A and B Gate 2: ___ gate, inputs Gate 1 and C

X = (NOT A) AND B Gate 1: ___ gate, input A Gate 2: AND gate, inputs Gate 1 and B

X = (A AND B) OR (B AND C) One gate per operator, so gates needed: _

X = (A OR B) AND C Gate 1 output and C feed the AND gate The AND gate output is labelled _

Spot the Error

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

Question 1

A X = (A AND B) OR C

B Gate 1: OR, inputs A and B

C Gate 2: OR, inputs G1 and C

D Gate 2 output is X

Question 2

A X = (A OR B) AND C

B Gate 1: OR, inputs A and B

C Gate 2: AND, inputs G1 and C

D Gate 1 output is X

Question 3

A X = (A AND B) OR (NOT C)

B Gate 1: AND, inputs A and B

C Gate 2: NOT, input C

D Gate 3: OR, inputs A and G2

E Gate 3 output is X

Question 4

A X = NOT (A AND B)

B Gate 1: AND, inputs A and B

C Gate 2: NOT, input A

D Gate 2 output is X

Question 5

A X = A OR (B AND C)

B Gate 1: AND, inputs A and B

C Gate 2: OR, inputs A and G1

D Gate 2 output is X

Answer Key

Creating a logic circuit from an expression

Section A: Quick Questions

A — The AND gate, because it is in the brackets

B — 2 gates: one AND and one OR

B — Directly to the OR gate

A — The AND gate

A — One NOT gate with A as its only input

Section B: Match the Pairs

X = (A AND B) OR C → Draw an AND gate for A and B first, then feed its output and C into a final OR gate that gives X

X = NOT (A OR B) → Draw an OR gate for A and B, then pass its output through a NOT gate to give X

Draw one gate for each operator, so an expression with two operators needs two gates joined by a wire → X = (A OR B) AND C

A NOT applied to a single input is drawn as a NOT gate on that input before it reaches the next gate → X = (NOT A) AND B

For X = (A AND B) OR C, drawing an OR gate for A and B, then an AND gate with C → The gates are swapped. The bracket contains AND, so A and B go into an AND gate first, and the OR gate comes last with C.

For X = (A OR B) AND C, drawing one AND gate with the inputs A, B and C and no OR gate → The OR in the bracket was left out. Every operator needs its own gate, so A and B must go into an OR gate whose output feeds the AND gate with C.

Section C: Definitions

X = (A AND B) OR C — Draw one gate per operator: the bracket (A AND B) becomes an AND gate first, and its output feeds the final OR gate along with C to give X.

Section D: Fill in the Blanks

X = (A AND B) OR C
Gate 1 (bracket): AND gate, inputs A and B
Gate 2: OR gate, inputs Gate 1 and C

X = (A OR B) AND C
Gate 1: OR gate, inputs A and B
Gate 2: AND gate, inputs Gate 1 and C

X = (NOT A) AND B
Gate 1: NOT gate, input A
Gate 2: AND gate, inputs Gate 1 and B

X = (A AND B) OR (B AND C)
One gate per operator, so gates needed: 3

X = (A OR B) AND C
Gate 1 output and C feed the AND gate
The AND gate output is labelled X

Section E: Spot the Error

B — The bracket (A AND B) must become an AND gate. Line 2 should read 'Gate 1: AND, inputs A and B'.

D — The final gate (the AND gate, Gate 2) produces X. Gate 1 only feeds into Gate 2. Line 4 should read 'Gate 2 output is X'.

D — The final OR gate must take the outputs of the two bracketed gates, G1 and G2, not the raw input A. Line 4 should read 'Gate 3: OR, inputs G1 and G2'.

C — NOT applies to the whole bracket, so the NOT gate takes the output of the AND gate (G1), not input A. Line 3 should read 'Gate 2: NOT, input G1'.

B — The bracket contains B and C, so the AND gate must take inputs B and C. Line 2 should read 'Gate 1: AND, inputs B and C'.