LED Dice
Our aim is to create an LED Dice using a breadboard and 7 LEDs disposed as follows:
![LED-Dice](https://www.101computing.net/wp/wp-content/uploads/LED-Dice.png)
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.
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LED 1 & 6 should be off for the following values:
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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](https://www.101computing.net/wp/wp-content/uploads/LED-Dice-1-Karnaugh-Map.png)
Karnaugh Map for LED 1 & LED 6
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LED 2 & LED 5 should be off for the following values:
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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](https://www.101computing.net/wp/wp-content/uploads/LED-Dice-2-Karnaugh-Map.png)
Karnaugh Map for LED 2 and LED 5
LED 3 & LED 4 (middle-left and middle-right) should be on for the following values:
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LED 3 & 4 should be off for the following values:
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LED 7 (in the middle) should be on for the following values:
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LED 7 should be off for the following values:
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LED Dice: Boolean Expressions
The Karnaugh maps will help us define the Boolean Expressions associated with each of the 7 LEDs.
![Karnaugh Map for LED 1 & 6](https://www.101computing.net/wp/wp-content/uploads/LED-Dice-1-Karnaugh-Map-blocks.png)
Karnaugh Map for LED 1 & LED 6
![Boolean Expression for LED1 & LED 6](https://www.101computing.net/wp/wp-content/uploads/LED-Dice-1-6-Boolean-Expression.png)
Boolean Expression for LED1 & LED 6
![Karnaugh Map for LED 2 & LED 5](https://www.101computing.net/wp/wp-content/uploads/LED-Dice-2-Karnaugh-Map-Blocks.png)
Karnaugh Map for LED 2 & LED 5
![Boolean expression for LED 2 & LED 5](https://www.101computing.net/wp/wp-content/uploads/LED-Dice-2-5-Boolean-Expression.png)
Boolean expression for LED 2 & LED 5
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.
![Boolean Expression for LED1 & LED 6](https://www.101computing.net/wp/wp-content/uploads/LED-Dice-1-6-Boolean-Expression.png)
Boolean Expression for LED1 & LED 6
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](https://www.101computing.net/wp/wp-content/uploads/LED-Dice-Logic-gates-1-6.png)
Logic Gates Diagram for LED 1 & LED 6
![Boolean expression for LED 2 & LED 5](https://www.101computing.net/wp/wp-content/uploads/LED-Dice-2-5-Boolean-Expression.png)
Boolean expression for LED 2 & LED 5
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](https://www.101computing.net/wp/wp-content/uploads/LED-Dice-Logic-gates-2-5.png)
Logic Gates Diagrams for LED 2 & LED 5
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.
![](https://www.101computing.net/wp/wp-content/uploads/dice-made-of-logic-gates.png)
You can also recreate the electronic circuit using bread boards, LEDs, resistors and logic gates or create your electronic cricuit online using tinkercad.
![unlock-access](/wp/wp-content/uploads/unlock-access.png)
Solution...
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