# LED Dice Logic Gates Diagrams

#### LED Dice

Our aim is to create an LED Dice using a breadboard and 7 LEDs disposed as follows:

We will then use three buttons/switches to control the 7 LEDs of the dice to recreate the following patterns:

#### Octal Number System

The octal numeral system, or oct for short, is the base-8 number system. It uses 8 digits from 0 to 7. Octal numerals can be converted into binary using 3 binary digits and the following conversion table.

We will use three input buttons A,B,C representing the 3 binary digits to generate 8 binary patterns representing the 8 octal digits from 0 to 7.

We will then use logic gates circuits to control each of the 7 LED based on the three inputs:

#### LED Dice: Truth Tables & Karnaugh Maps

We will use three inputs A,B and C to represent the three digits as ABC (A is the most significant digit, C is the least significant digit). When creating the electronic circuit we will use 3 switches to represent these 3 inputs.

We will need 7 outputs one for each LED. So let’s investigate each LED one at a time.

LED 1 & 6LED 2 & 5LED 3 & 4LED 7
LED 1 & LED 6 (top-left and bottom right) should be on for the following values:

 ABC:100 ABC:101 ABC:110 ABC:111

LED 1 & 6 should be off for the following values:

 ABC:000 ABC:001 ABC:010 ABC:011

Hence the Truth Table for LED 1 & LED 6 is as follows:

 Inputs Output A B C LED 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1

This Truth table can be represented using a Karnaugh Map:

Karnaugh Map for LED 1 & LED 6

LED 2 & LED 5 (top-right and bottom left LED) should be on for the following values:

 ABC:010 ABC:011 ABC:100 ABC:101 ABC:110 ABC:111

LED 2 & LED 5 should be off for the following values:

 ABC:000 ABC:001

Hence the Truth Table for LED 2 & LED 5 is as follows:

 Inputs Output A B C LED 2 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1

This Truth table can be represented using a Karnaugh Map:

Karnaugh Map for LED 2 and LED 5

Follow the same process to define the Truth Table and Karnaugh Map of LED 3 and LED 4 which have the same truth table.

LED 3 & LED 4 (middle-left and middle-right) should be on for the following values:

 ABC:110 ABC:111

LED 3 & 4 should be off for the following values:

 ABC:001 ABC:010 ABC:011 ABC:100 ABC:101 ABC:000

Follow the same process to define the Truth Table and Karnaugh Map of LED 7 (LED in the middle of the dice).
LED 7 (in the middle) should be on for the following values:

 ABC:001 ABC:011 ABC:101 ABC:111

LED 7 should be off for the following values:

 ABC:100 ABC:000 ABC:010 ABC:110

#### LED Dice: Boolean Expressions

The Karnaugh maps will help us define the Boolean Expressions associated with each of the 7 LEDs.

LED 1 & 6LED 2 & 5LED 3 & 4LED 7
Karnaugh Map:

Karnaugh Map for LED 1 & LED 6

Boolean Expression:

Boolean Expression for LED1 & LED 6

Karnaugh Map:

Karnaugh Map for LED 2 & LED 5

Boolean Expression:

Boolean expression for LED 2 & LED 5

Use the Karnaugh Map for LED 3 & 4 to define the Boolean Expression of LED 3 & LED 4.
Use the Karnaugh Map for LED 7 to define the Boolean Expression of LED 7.

#### LED Dice: Logic Gates Diagrams

We can now convert each Boolean expression into a Logic Gates circuit to link our 3 inputs (switches) to our 7 LEDs display using a range of logic gates.
LED 1 & LED 6LED 2 & LED 5LED 3 & LED 4LED 7
Boolean Expression:

Boolean Expression for LED1 & LED 6

Logic Gates Diagram:
In this case, the Boolean expression being so basic, there is no need for any logic gates to control LED 1. The LED is directly connected to input A.

Logic Gates Diagram for LED 1 & LED 6

Boolean Expression:

Boolean expression for LED 2 & LED 5

Logic Gates Diagram:
In this case, the Boolean expression being so basic, only one OR gate is needed using input A and input B.

Logic Gates Diagrams for LED 2 & LED 5

Use the Boolean Expression of LED 3 & LED 4 to draw the logic gates diagram required to control LED 3 & LED 4.
Use the Boolean Expression of LED 7 to draw the logic gates diagram required to control LED 7.

#### Testing

You can now recreate your logic gates circuit using our logic gates circuit simulator to test if it behaves as expected for all 8 entries.

You can also recreate the electronic circuit using bread boards, LEDs, resistors and logic gates or create your electronic cricuit online using tinkercad.

LED Dice – Electronic Circuit – Using AND and OR gates.

#### Solution...

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