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BCD to Excess-3 Code Converter
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Quick Overview -
Beginner's Guide to understand Conversion,
BCD to Excess -3 code Converter / Conversion using K-map,
Making truth table and find output expressions,
Finding Don't care conditions,
Output Dependencies,
Implementation using gates.
Truth Table -
Since BCD code is from 0 to 9. So for each BCD input there will be output +3 greater than the bcd. So for BCD ( 0 0 0 0 ) there will be output (0 0 0 0 + 0 0 1 1) which is equals to (0 0 1 1).
To get output table (truth table) add 3 (0 0 1 1) in each BCD input.
Now, Once truth table is ready go for next step.
Method -
From table we will make ouput expressions which can be solved using k-map (Karnaugh Map).
To get expression. Start taking one output bit. lets take E3 (You are free to choose anyone first).
Now, look at the truth table and find 1's in E3 column and corresponding BCD code.
find decimal value for this BCD code.
Now, write it as E3 = Σm(6,7,8,9) .
Similarly E2 ,E1 ,E0 can be found .
E3 = Σm(6,7,8,9)
E2 = Σm(2,3,4,5)
E1 = Σm(0,1,4,5,8,9)
E0 = Σm(1,3,5,7,9)
Since BCD is only from 0 to 9, therefore for input 10 to 15 output will be don't care terms.
So, write outputs also in terms of don't care conditions -
E3 = Σm(6,7,8,9) + dm(10,11,12,13,14)
Similarly E2 ,E1 ,E0 can be expressed.
Output Expressions -
E3 = Σm(6,7,8,9) + dm(10,11,12,13,14)
E2 = Σm(2,3,4,5) + dm(10,11,12,13,14)
E1 = Σm(0,1,4,5,8,9) + dm(10,11,12,13,14)
E0 = Σm(1,3,5,7,9) + dm(10,11,12,13,14)
K-map For E3 -
E3 = Σm(6,7,8,9) + dm(10,11,12,13,14)
E3 = B2B0 + B2B1 + B3
K-map For E2 -
E2 = Σm(2,3,4,5) + dm(10,11,12,13,14)
E2 =B2'B0 + B2'B1 + B2B1'B0'
K-map For E1 -
E1 = Σm(0,1,4,5,8,9) + dm(10,11,12,13,14)
E1 = B1B0 + B1'B0'
K-map For E0 -
E0 = Σm(1,3,5,7,9) + dm(10,11,12,13,14)
E0 = B0'
Boolean Expressions For Outputs E3 , E2 , E1 , E0 -
E3 = B2B0 + B2B1 + B3
E2 = B2'B0 + B2'B1 + B2B1'B0'
E1 = B1B0 + B1'B0'
E0 = B0'
Implementation Using Basic Gates -
