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BCD to Excess-3 converter
BCD to Excess-3 converter

Digital Logic Circuits

Code converter | BCD to Excess-3 converter

BCD to Excess-3 converter

In this post on a code converter, we are going to see BCD to Excess-3 converter using the k-mapping technique.

If you are new to this topic BCD to Excess-3 Converter, better have a look on to Study of Logic Gates

BCD to Excess-3 using K-map.

 

BCD to Excess-3 conversion:

                             BCD INPUT                       EXCESS-3 OUPUT
      B3       B2      B1        B0       E3      E2       E1       E0
0 0 0 0 0 0 1 1
0 0 0 1 0 1 0 0
0 0 1 0 0 1 0 1
0 0 1 1 0 1 1 0
0 1 0 0 0 1 1 1
0 1 0 1 1 0 0 0
0 1 1 0 1 0 0 1
0 1 1 1 1 0 1 0
1 0 0 0 1 0 1 1
1 0 0 1 1 1 0 0
1 0 1 0 X X X X
1 0 1 1 X X X X
1 1 0 0 X X X X
1 1 0 1 X X X X
1 1 1 0 X X X X
1 1 1 1 X X X X

A BCD (Binary Coded Decimal) can be converted into Excess-3 by

Taking the 3 rd value as a start and continue up to 9. After the 9, make it as a don’t care.

A don’t care is a condition which can be used in K-mapping technique.

There is no necessity for all the don’t care should be mapped, a don’t care should be mapped only if it is needed.

All the procedure for mapping remains the same.

Code conversions, excess-3 to BCD converter

K-map for E3:

BCD to Excess-3 converter

Here K-mapping is done with the don’t care conditions.

Here on the red framed section, there is two 1’s. Here don’t care condition also mapped because to make it a higher possibility of mapping i.e 8.

(You should always map towards a higher possibility)

Next, to 8, the preference should be given to 4.

The green framed and a blue framed section has the mapping of 4 respectively.

Logic Gates, Logic Gate Symbols, diagram, truth table

K-map for E2:

BCD to Excess-3 converter

Here the mapping is done for 4 elements and 2 elements since there is no availability for mapping the 8 elements.

(Mapping can be done anyways like the above k-map, elements are mapped with the first row and last row.

Mapping can also be done for the first column and last column if it is necessary.)

 Gray code -> binary converter

K-map for E1:

BCD to Excess-3 converter

Here the mapping is done for 4 elements since there is no possibility for 8 elements mapping. On the third column don’t care is included because to make the preference to 4.

Code conversion | Gray code -> binary converter

K-map for E0:

BCD to Excess-3 converter

Here also the mapping is done for 4 elements.

Binary to gray code converter

Logic Diagram: 

BCD TO EXCESS 3 LOGIC DIAGRAM

 

Remember don’t care conditions should be mapped only if it is necessary to make higher order mapping.

Note: 

On can get a different logic diagram rather than the one which was shown above because of simplifaction. Don’t worry about the logic, just draw a logic diagram as per your simplified value.

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