Logic Gates & Logic Circuits (Cambridge International AS Computer Science): Exam Questions

A security system has both a floodlight (very bright light) and an audio alarm.

The data from multiple sensors is analysed and used to:

• turn on the floodlight
• sound the audio alarm.

Sensors can be used to detect:

• if doors are open
• the external daylight level
• if people are detected within a set distance.

The floodlight (X) and audio alarm (Y) operate according to the following criteria:

The floodlight turns on (X = 1) if:

• the security system is switched on and
• the external daylight level is low and
• a person is detected within 2m.

The audio alarm turns on (Y = 1) if:

• the security system is switched on and
• one or more doors are open, or a person is detected within 2m.

Write logic expressions for the security system.

Complete the truth table for the logic expression:

X = (A XOR B) NAND (A AND (B XOR C))

Draw the logic circuit for the logic expression:

W = P NAND ((Q OR NOT R) XOR (P XOR Q))

Describe the operation of a 2-input XOR gate.

Write the logic expression for the following logic circuit.

Draw the logic circuit for the logic expression:

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

Tick (✓) one box to identify the correct logic statement for this truth table.

☐ NOT (A AND B AND C)

☐ (A XOR B) NOR C

☐ (A OR B OR C) NOR C

☐ NOT A AND NOT B AND NOT C

Draw a logic circuit for the logic expression:

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

Describe the operation of each of the following logic gates:

NAND .......................

NOR ........................

XOR .........................

OR ..........................

Draw a logic circuit for this logic expression:

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

Each of the following truth tables has three inputs (A, B and C) and one output (X).

Draw one line to match each truth table with its logic expression.

The diagram shows a logic circuit.

Complete the truth table for the given logic circuit. Show your working.

The diagram shows a logic circuit.

Complete the truth table for the given logic circuit. Show your working.

Complete the truth table for the logic expression:

X = NOT (A NAND B) XOR (NOT B AND (B NOR C))

Draw a logic circuit for the logic expression:

X = (A AND NOT (B OR C)) AND (B NOR C)

Write the Boolean expression that corresponds to the following logic circuit.

Complete the truth table for the logic expression:

X = A XOR (B AND (A NAND B) AND NOT C)

Complete the truth table for the logic expression:

Y = ((P AND Q) XOR ((NOT Q) OR R)) AND NOT P

Draw a logic circuit for the logic expression:

Y = ((P AND Q) XOR ((NOT Q) OR R)) AND NOT P

This diagram represents a logic circuit.

Complete the truth table for the given logic circuit.