# Digital Design

Digital Design

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## Karnaugh Map Gray and Binary Code

#### Lakshmi Manasa

##### Newbie In K-Map, Gray codes are used as shown below (00,01,11,10). But why is the decimal equivalent of binary code written inside the box instead of the decimal equivalent of Gray code? (For e.g., First row, third column box should be written as 2, right? Since 011 is Gray code, its decimal value is 2). When we have 3 as min term, we add a 1 to First row third column instead of First row 4th column. Please clarify this. #### wwfeldman karnaugh maps are annotated in gray code so that the inputs along the top and along the left side
change in only one bit to any neighboring box (left right, up down, and wrap around) .

the decimal numbers you have in the lower right corners are the decimal equivalents of the
annotations, in binary

i expect you need to fill in the output you want in each box, then analyze
the decimal equivalents help ensure the correct row from the truth table,
which usually lists the inputs in binary, and hence the outputs are ordered in bunary

#### ELECTRONICIENSENIOR

##### Member level 2 The utility of Karnaugh tables is to help finding logical equations. The binary values represent the inputs, for example A and B horizontally, and C vertically. In eack box of the map you put the value expected for Z output.

The Gray code has been established because two signal transitions cannot arrive simunaously. The best illutration is a rotary coder, as for time in many microwave oven, or axis of mechanical mouses.

After that you encircle same values. It is explained here :

I have studied that when I was 16 years old.

#### crutschow Since 011 is Gray code, its decimal value is 2
Gray code is a particular sequence of numbers but the numbers are still binary, so 011 is still decimal 3.

#### KlausST

##### Super Moderator
Staff member Hi,

It's a question of representation.

What do you want to show .. and how is it represented.
Indeed in the case of post#1 ... if the carnaugh internal number should represent the "gray coded value" I'd expect that:
"11" (Gray) = 2 decimal.

So in the end such a diagram needs some context. We don't have. We don't know the autor's thoughs.

--> Posting just the diagram is useless.

We can only guess: The diagram is from a school book, maybe homework, and needs to be filled correctly.
So "why filled"?
Because the box holds a value like "3". Now "3" is neither binary, nor is it a single bit.
It just is the "field numbering" ... maybe for the teacher to ensure to get identical Karnaugh diagrams from all pupils to ease his/her work.

The true content of Karnaugh box should be:
* just a single bit binary value = logic HIGH/LOW or 1/0.

So for a 3 bit Gray code you need 3 such diagrams:
* for the LSB
* for the MSB
* and for the bit inbetween

Klaus

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