Code Conversion | Binary to Gray Code Converter
In this post on a code conversion, we are going to see Binary to Gray Code conversion using K-map technique.
If you are new to this topic (Digital Logic Circuits), I recommend you to have a look at my previous topic the Study of Logic Gates before reading this topic.
Binary to gray code converter:
| BINARY INPUT | GRAY CODE OUTPUT | ||||||
| B3 | B2 | B1 | B0 | G3 | G2 | G1 | G0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 |
| 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 |
| 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 |
| 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 |
| 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 |
| 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 0 | 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 |
A binary code can be converted into a gray code by using this following strategy.
The binary code for 2 is oo10.
The Gray code for 2 is 0011.
Now let us see how to convert binary code to a gray code.
0 + 0 + 1 + 0
0 0 1 1
Firstly, start from the left-hand side and add both bits. so
0+0 = 0
0+0 =0
0+1 = 1
1+0 = 1
If 1+1 = 10 , here 1 is carry and it should be added with next bit.
Now let us do Karnaugh Mapping. (K – map)
Code Conversion | Excess-3 -> BCD converter
K- map for G3:
The first preference should be given to 8 pairs so 8 pairs are mapped together in the above k- mapping.
G3 = B3
Code Converter | BCD -> Excess-3 Converter
K- map for G2:
Since there is no availability of 8 pairs we cannot map 8 elements. The second preference should be given to 4 so only the 4 elements are mapped together in the k-mapping for G2.
K- map for G1:
Here also the 4 elements are mapped because there is no possibility for mapping 8 elements. The four elements can be mapped anyway like the one which is shown here. The only thing is it should be adjacent.
Code Converter | Gray Code -> Binary using K-map
K – map for Go:
Since there is no availability for 8 elements mapping we can’t map elements. The next preference which is 4 elements mapping that can be done as there is an existence of 2 ( 4 pairs of elements).
Note:
If there is no availability of 4 elements to map, the next preference should be given to 2 elements.
If there is no availability of 2 elements to map, the next preference should be given to 1 element.
logic gates | logic gate | symbols logic diagram | truth table
Logic Diagram:
That’s the process on Binary to Gray Code Converter.
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