Logic Gates Circuits

This set of challenges is designed to be completed with a logic board such as the Logic & Arithmetic board designed by the University of Southampton and the UK Electronic Skills Foundation.

Alternatively, if you do not have access to a physical kit, you can still complete these challenges using the logic.ly online logic gates circuit simulator.

Step 1: The Main Logic Gates

For each of the main logic gates, recreate the circuit as it appears on the diagram. Then use your circuit to compete the truth table for the logic gate.

NOT GateAND GateOR GateXOR GateNAND GateNOR Gate
logic-board-not-gate
Truth Table:

Input J Output X
0
1
logic-board-and-gate
Truth Table:

Input J Input K Output X
0 0
0 1
1 0
1 1
logic-board-or-gate
Truth Table:

Input J Input K Output X
0 0
0 1
1 0
1 1
logic-board-xor-gate
Truth Table:

Input J Input K Output X
0 0
0 1
1 0
1 1
logic-board-nand-gate
Truth Table:

Input J Input K Output X
0 0
0 1
1 0
1 1
logic-board-nor-gate
Truth Table:

Input J Input K Output X
0 0
0 1
1 0
1 1

Step 2: Logic Gates Circuits

By combining multiple logic gates together you can create a circuit that will “behave” a certain way. To record how the circuit “behaves” for any given set of inputs we use a Truth Table. For instance you can complete the Truth table for the following circuit:

Logic Gates Circuit
logic-board-circuit-1
Truth Table:

Input J Input K Input L Output X
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

Step 3: Logic Problems

Your task is to create and test a logic gate circuit for each of the given problems:

Car LightBurglar AlarmSmartphone Ringtone
car-3-doors
A small car has 3 doors: 2 front doors and a hatchback. The internal light of the car is on when any of the car doors is open.

Create and test a logic gates circuit to control the internal light (X) of the car based on whether a door (J, K or L) is open (1) or closed (0).

Input J Input K Input L Output X
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
burglar-alarmA burglar alarm has three inputs:

  • Input J: Whether the burglar alarm is activated (1) or not (0).
  • Input K: A motion sensor can detect movement (1) or not (0).
  • Input L: A door sensor can detect if the front door is open (1) or is closed (0).

The alarm siren (X) should be on if the alarm is activated and the motion sensor detects a movement or the door sensor detects that the door is open.

Create and test a logic gates circuit to control the siren of this burglar alarm based on the three inputs J,K and L.

Input J Input K Input L Output X
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
incoming-call
A smartphone ringtone is played only if:

  • The phone is receiving an incoming call. (input J = 1)
  • The phone sound is on. (input K = 1)
  • The phone is not on airplane mode. (input L = 0)

Create and test a logic gates circuit to control whether the ringtone of a smartphone is on (X=1) or not (X=0) based on the three inputs J, K, L.

Input J Input K Input L Output X
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

Extension Task: The Mystery Gate!

Mystery Gate
logic-gates-simplify-circuit
The above logic gates circuit can be replaced by one single logic gate! Recreate this circuit on your logic board to test it and complete its truth table. Then find out what logic gate has the same truth table as this complex circuit.
Truth Table:

Input J Input K Output X
0 0
0 1
1 0
1 1

Logic Gate:

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