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Logisim software program need help prime numbers by
Logisim software program need help
Prime numbers by definitions are natural numbers that are divisible only to themselves and 1. Prime numbers are: 2,3,5,7,11,13,17,19,23,29,31,...
In this project, you are do design a combinational logical circuit that can recognize prime numbers from 0 to 30.
The input to your circuit will be a number in binary format with 5 bits, ABCDE, representing the binary equivalent of number 0,1,2,3,4,5,....,29,30. The output for your circuit will be the value of 1 (representing that the input number is a prime number) or 0 (representing that the input number is not a prime number).
You need to create a truth table for your problem. Then use Kaurnaugh map to find the simplified combinational logical circuit. You will then need to build a simulation of the simplified circuit using the Logisim software (introduced in Week 4 folder). You may test your circuit to make sure that it correctly recognizes all prime numbers in the range of 0-30.
Answers :
To recognize prime numbers from 0 to 30 using a combinational logic circuit, we'll follow these steps:
Step 1: Prime Number Identification
Identify prime numbers between 0 and 30. These are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
Step 2: Binary Representation
List each number from 0 to 30 along with its 5-bit binary representation:
0 -> 00000
1 -> 00001
2 -> 00010 (prime)
3 -> 00011 (prime)
4 -> 00100
5 -> 00101 (prime)
6 -> 00110
7 -> 00111 (prime)
8 -> 01000
9 -> 01001
10 -> 01010
11 -> 01011 (prime)
12 -> 01100
13 -> 01101 (prime)
14 -> 01110
15 -> 01111
16 -> 10000
17 -> 10001 (prime)
18 -> 10010
19 -> 10011 (prime)
20 -> 10100
21 -> 10101
22 -> 10110
23 -> 10111 (prime)
24 -> 11000
25 -> 11001
26 -> 11010
27 -> 11011
28 -> 11100
29 -> 11101 (prime)
30 -> 11110
Step 3: Truth Table
Create a truth table using 5 input bits ABCDE and 1 output P where P = 1 for prime numbers and 0 otherwise.
| A | B | C | D | E | P (prime) |
|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 1 | 0 | 1 |
| 0 | 0 | 0 | 1 | 1 | 1 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 1 | 1 |
| 0 | 0 | 1 | 1 | 0 | 0 |
| 0 | 0 | 1 | 1 | 1 | 1 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 1 | 0 | 0 |
| 0 | 1 | 0 | 1 | 1 | 1 |
| 0 | 1 | 1 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 1 | 0 | 0 |
| 0 | 1 | 1 | 1 | 1 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 1 | 1 |
| 1 | 0 | 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 | 1 | 0 |
| 1 | 0 | 1 | 1 | 0 | 0 |
| 1 | 0 | 1 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 | 0 | 0 |
| 1 | 1 | 0 | 1 | 1 | 0 |
| 1 | 1 | 1 | 0 | 0 | 0 |
| 1 | 1 | 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 | 0 | 0 |
Step 4: Karnaugh Map
Plot the output (P) on a Karnaugh map to simplify the logic expression. Group 1s to find simplified logic equations.
Step 5: Simplified Logic Expression
After solving the Karnaugh map, derive the simplified logic expression representing the prime outputs.
Step 6: Logisim Implementation
Use the simplified logic expression from the Karnaugh map to construct the circuit in Logisim.
Step 7: Testing
Verify that your Logisim circuit correctly identifies prime numbers by running different input cases.
By following these steps, you can achieve the design of a combinational logical circuit to recognize prime numbers using Logisim. If you need additional guidance on using Logisim itself, you may refer to its documentation or tutorials available online.
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