Using knrnaugh maps to design a circuit

In summary, the conversation discusses the design of a circuit to convert a number in Excess-3 code to BCD using Karnaugh maps. The conversation also mentions the use of a truth table to develop the circuit and provides a sample truth table with inputs and outputs. The individual also recommends practicing Karnaugh map implementation and suggests using a textbook or attending class for further understanding.
  • #1
MasterWu77
21
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Homework Statement



Design a circuit to covert a number represented in Excess-3 code to BCD. You must use karnaugh maps in this problem. provide a circuit diagram as well.

Homework Equations



Using the karnaugh man

The Attempt at a Solution



I understand the basics of a Karnaugh map but I'm not sure of how to turn a karnaugh map into a circuit. What exactly is an excess 3 code and how would i use that to make my circuit?
 
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  • #2
http://en.wikipedia.org/wiki/Excess-3

from this info you can develop a truth table for your excess-3 inputs, with 5 output columns also in the truth table, one for each digit of the BCD number.
Something like: A-D = inputs, Fs = outputs
A B C D F4 F3 F2 F1 F0
0 0 0 0 1 1 1 0 1
0 0 0 1 1 1 1 1 0
0 0 1 0 1 1 1 1 1
0 0 1 1 0 0 0 0 0
0 1 0 0 0 0 0 0 1
etc etc
1 1 1 1 0 1 1 0 0

In this case I've put in the 5th output (F4) as a sign indicator, where 1 signifies the BCD value is negative. I've used 2s complement form to determine BCD for the negative excess-3 values.
A = MSB of input, D = LSB of input (Excess-3)
F4 = MSB of output, F0 = LSB of output (BCD)

From this truth table you can write up a K-map for each output F4 through F0. Simplest way is probably just get sum of products form for each output and do a quick AND/OR implementation for each output line, given the 4 inputs. If you want to simplify you can collect like terms as you desire.

If you don't know how to turn a K-map into a circuit you should probably revise that a lot. It's quite simple and you should do lots of practice to make it easy for yourself. It's too detailed for me to bother going into it here. Try your school library for a suitable textbook or just go to class more often.

EDIT: If either of my method or interpretation are wrong please excuse me! only in 1st year electrical eng course and it's late at night right now.
 
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  • #3
Wow you are smart hahaha...I'm just starting to understand this in class a little bit, but you seems to know what you talking about. I'm lost, but you guys have a lot of knowledge. I'm a noobie lol...Interesting.
 
  • #4
Good luck! If you've just started the class don't worry it'll all soon make semse ;) good luck!
 

FAQ: Using knrnaugh maps to design a circuit

1. What is a Karnaugh map?

A Karnaugh map, also known as a K-map, is a graphical method used to simplify boolean algebra expressions for designing digital circuits. It is a visual tool that helps to identify and eliminate redundant terms in a boolean expression.

2. How do I use a Karnaugh map to design a circuit?

To use a Karnaugh map, you first need to create a truth table for the boolean expression representing your circuit. Then, transfer the values from the truth table onto the K-map, grouping the cells with the same value into squares or rectangles. Finally, write the simplified boolean expression using the grouped terms to design your circuit.

3. What are the benefits of using Karnaugh maps for circuit design?

Karnaugh maps offer several benefits for circuit design, including simplifying boolean expressions, reducing the number of logic gates needed, and minimizing the chances of errors. They also provide a visual representation of the circuit, making it easier to understand and troubleshoot.

4. Are there any limitations to using Karnaugh maps for circuit design?

Karnaugh maps are best suited for designing circuits with a small number of variables (usually up to 5). They can become more complex and time-consuming for circuits with a larger number of variables. Additionally, K-maps are not useful for all types of boolean expressions and may not always provide the most efficient design.

5. How do I know if I have correctly designed my circuit using a Karnaugh map?

You can check the correctness of your circuit design by comparing the outputs of the original boolean expression with the simplified expression you obtained using the K-map. Additionally, you can use simulation tools to test your circuit and ensure it functions as intended.

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