Creating a logic circuit from a truth table

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Quick Questions

Shade in the A or B circle for each question.

1. A truth table for inputs A and B has X = 0, 0, 0, 1 for rows 00, 01, 10, 11. What is the first step to draw the circuit?

A Write the expression X = A AND B

B Draw an OR gate and test it

2. A table with inputs A and B has X = 1, 0, 0, 0 for rows 00, 01, 10, 11. Which expression gives this X column?

A X = A NOR B

B X = A NAND B

3. A table with inputs A and B has X = 0, 1, 1, 0 for rows 00, 01, 10, 11. Which expression do you write?

A X = A XOR B

B X = A OR B

4. A table has X = 1, 1, 1, 0 for rows 00, 01, 10, 11. Which circuit do you draw from the expression X = NOT (A AND B)?

A A NOT gate on A and a NOT gate on B, then an AND gate

B An AND gate whose output goes into a NOT gate

5. The expression for a table is X = (A AND B) OR C. How many gates do you draw?

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

B 2 gates: one AND and one OR

Match the Pairs

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

Left column		Right column
1X = NOT A		ADraw an OR gate for A and B, then feed its output and input C into an AND gate. That is two gates, one per operator.
2X = (A OR B) AND C		BX = A OR B
3Single-gate table: X is 1 when at least one of A and B is 1, so the expression needs just one OR gate.		COR would also give 1 when only one input is 1, but the table has a 1 only on the row where both are 1. The expression should be X = A AND B.
4Three-input table: X is 1 when A and B are both 1, or when C is 1. Write both parts, join them and do not simplify.		DThe expression for a table where X is always the opposite of A. Draw one NOT gate.
5Table: X = 1 only when A = 1 and B = 1. Expression written: X = A OR B		EX = (A AND B) OR C
6Circuit for X = (A AND B) OR C drawn with a single AND gate		FOnly one gate was drawn. The expression has two operators, so the circuit needs an AND gate and an OR gate, with the AND output going into the OR gate along with C.

Definitions

X = (A AND B) OR C

Fill in the Blanks

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

X = A ___ B

X = ___ A

X = (A AND B) __ C

X = (A OR B) ___ C

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

Spot the Error

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

Question 1

A A B | X

B 0 0 | 0

C 0 1 | 1

D 1 0 | 0

E 1 1 | 1

F X = A AND B

Question 2

A A B | X

B 0 0 | 1

C other rows | 0

D X = NOT A OR B

E Gates: one OR, then one NOT

Question 3

A X = A AND (B OR C)

B Gate 1: A AND B

C Gate 2: result OR C

D Row A=0,B=0,C=1 gives X=1

Question 4

A A B C | X

B 1 1 0 | 1

C 0 0 1 | 0

D X = (A AND B) OR C

E Draw an AND gate, then an OR gate

Question 5

A 1 Simplify the expression

B 2 Draw one gate per operator

C 3 Do not simplify it

D 4 Check against the table

Answer Key

Creating a logic circuit from a truth table

Section A: Quick Questions

A — Write the expression X = A AND B

A — X = A NOR B

A — X = A XOR B

B — An AND gate whose output goes into a NOT gate

B — 2 gates: one AND and one OR

Section B: Match the Pairs

X = NOT A → The expression for a table where X is always the opposite of A. Draw one NOT gate.

X = (A OR B) AND C → Draw an OR gate for A and B, then feed its output and input C into an AND gate. That is two gates, one per operator.

Single-gate table: X is 1 when at least one of A and B is 1, so the expression needs just one OR gate. → X = A OR B

Three-input table: X is 1 when A and B are both 1, or when C is 1. Write both parts, join them and do not simplify. → X = (A AND B) OR C

Table: X = 1 only when A = 1 and B = 1. Expression written: X = A OR B → OR would also give 1 when only one input is 1, but the table has a 1 only on the row where both are 1. The expression should be X = A AND B.

Circuit for X = (A AND B) OR C drawn with a single AND gate → Only one gate was drawn. The expression has two operators, so the circuit needs an AND gate and an OR gate, with the AND output going into the OR gate along with C.

Section C: Definitions

X = (A AND B) OR C — To draw a circuit from a truth table, write the expression that gives the X output column, then draw one gate for each operator in it. Do not simplify the expression.

Section D: Fill in the Blanks

X = A AND B

X = NOT A

X = (A AND B) OR C

X = (A OR B) AND C

X = (A AND B) OR C
Gates to draw: 2

Section E: Spot the Error

C — The expression X = A AND B gives 1 only when both inputs are 1. The row 0 1 must therefore give X = 0, so the line should be '0 1 | 0'.

D — Without brackets, NOT applies only to A. The NOT must apply to the result of A OR B, so the line should be 'X = NOT (A OR B)'.

A — The expression must match the gates described: A AND B first, then OR C. The brackets belong round A AND B. The broken version gives X = 0 for the row 0 0 1, but the table says X = 1. It should be 'X = (A AND B) OR C'.

C — The expression has OR C, so whenever C = 1 the output X must be 1. The row 0 0 1 must give X = 1, so the line should be '0 0 1 | 1'.

A — The first step is to write the expression that gives the X column, not to simplify it. Step 3 says not to simplify, so the line should be '1 Write the expression for X'.