Drawing circuits without simplification

Name:

Date:

Class:

Quick Questions

Shade in the A or B circle for each question.

1. You are asked to draw a circuit for X = (A AND B) OR (A AND C). How many gates should your circuit contain?

A Three: two AND gates and one OR gate

B Two: A AND (B OR C) is shorter

2. A student draws a circuit with fewer gates than the expression has operators. The truth table is still identical. What mark outcome is likely?

A Marks lost: the circuit does not match the expression

B Full marks: the truth table is the same

3. The expression is X = NOT (A OR B). Which circuit is correct?

A An OR gate with its output going into a NOT gate

B A single NOR gate

4. The expression is X = (A AND B) OR NOT C. How many gates are needed?

A Two: AND and OR, because NOT C can be left out

B Three: AND, NOT and OR

5. True or false: you should simplify an expression before drawing its circuit, to save gates.

A True: shorter circuits are always preferred

B False: draw the circuit exactly as the expression is written

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 (A AND C)		AX = (NOT A AND B) OR C
2X = NOT (NOT A)		BDraw two NOT gates in a row. Do not remove them, even though the output is the same as A.
3Every operator in the expression needs its own gate, so this expression needs one NOT, one AND and one OR gate		CThe student removed the OR gate and one AND gate because both brackets are the same. The expression has three operators, so the circuit needs three gates.
4A circuit with the same truth table is not enough, because the circuit must use the gates of the given expression, such as an AND gate and an OR gate in this one		DThe student combined the NOT and AND operators into one NAND gate. The expression has two operators, so it needs two gates: an AND gate followed by a NOT gate.
5Expression: X = (A AND B) OR (A AND B). Circuit drawn: one AND gate only, with output X		EDraw two AND gates and one OR gate, three gates in total. Do not factor it into A AND (B OR C).
6Expression: X = NOT (A AND B). Circuit drawn: one NAND gate with output X		FX = (A OR B) AND (A OR C)

Definitions

one gate per operator

Fill in the Blanks

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

X = (A AND B) OR (A AND C) Gates to draw: _ (two AND, one OR)

X = NOT (A AND B) Draw AND then NOT, not one ____ gate

X = (A OR B) AND (A OR B) Gates: OR, OR and ___

X = A AND (B OR C) Rule: one gate for each ________

X = NOT (NOT A) Draw ___ NOT gates in series

Spot the Error

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

Question 1

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

B Gate 1: AND takes A and B

C Gate 2: OR takes Gate 1 and C

D Gates needed: 1

Question 2

A Rule: use the fewest gates

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

C Gates: AND, AND, OR

D Draw all 3 gates

Question 3

A Draw: X = NOT (A AND B)

B Gate 1: AND takes A and B

C Gate 2: NOT takes Gate 1

D Merge AND and NOT into NAND

Question 4

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

B Gate 1: AND takes A and B

C Gate 2: AND takes Gate 1, C

D Gates needed: 2

Question 5

A Draw: X = (NOT A) OR B

B Gate 1: NOT takes A

C Gate 2: OR takes A and B

D Gates needed: 2

Answer Key

Drawing circuits without simplification

Section A: Quick Questions

A — Three: two AND gates and one OR gate

A — Marks lost: the circuit does not match the expression

A — An OR gate with its output going into a NOT gate

B — Three: AND, NOT and OR

B — False: draw the circuit exactly as the expression is written

Section B: Match the Pairs

X = (A AND B) OR (A AND C) → Draw two AND gates and one OR gate, three gates in total. Do not factor it into A AND (B OR C).

X = NOT (NOT A) → Draw two NOT gates in a row. Do not remove them, even though the output is the same as A.

Every operator in the expression needs its own gate, so this expression needs one NOT, one AND and one OR gate → X = (NOT A AND B) OR C

A circuit with the same truth table is not enough, because the circuit must use the gates of the given expression, such as an AND gate and an OR gate in this one → X = (A OR B) AND (A OR C)

Expression: X = (A AND B) OR (A AND B). Circuit drawn: one AND gate only, with output X → The student removed the OR gate and one AND gate because both brackets are the same. The expression has three operators, so the circuit needs three gates.

Expression: X = NOT (A AND B). Circuit drawn: one NAND gate with output X → The student combined the NOT and AND operators into one NAND gate. The expression has two operators, so it needs two gates: an AND gate followed by a NOT gate.

Section C: Definitions

one gate per operator — Draw every gate in the given expression, one for each operator, even if a shorter circuit has the same truth table. Never combine or remove gates.

Section D: Fill in the Blanks

X = (A AND B) OR (A AND C)
Gates to draw: 3 (two AND, one OR)

X = NOT (A AND B)
Draw AND then NOT, not one NAND gate

X = (A OR B) AND (A OR B)
Gates: OR, OR and AND

X = A AND (B OR C)
Rule: one gate for each operator

X = NOT (NOT A)
Draw two NOT gates in series

Section E: Spot the Error

D — The expression has two operators, AND and OR, so the circuit needs two gates. It must not be squashed into one gate. It should say: Gates needed: 2.

A — The circuit must be drawn exactly as the expression is given, with one gate for each operator. It must not be cut down to the fewest gates. It should say: Rule: one gate per operator.

D — The expression uses an AND operator and a NOT operator, so both gates must be drawn. Combining them into one NAND gate breaks the rule. It should say: Keep AND and NOT as two gates.

B — The bracket (A OR B) needs an OR gate for A and B, not an AND gate. It should say: Gate 1: OR takes A and B.

C — The OR gate must take the output of the NOT gate, not A directly. Otherwise the NOT gate has been removed from the circuit. It should say: Gate 2: OR takes Gate 1 and B.