Excess 3 to bcd converter

The easy way to understand Excess 3 to BCD converter.

1. Excess-3 to b.c.d converter

2. contents BCD EXCESS-3 EXCESS-3 TO BCD OBSERVATION CIRCUIT

3. BCD BCD stands for Binary Coded Decimal. 0-9 are valid BCD’s If the number is two digit write binary of each digit separately. DIGIT BINARY BCD 0000 0000 1 0001 0001 2 0010 0010 3 0011 0011 4 0100 0100 5 0101 0101 6 0110 0110 7 0111 0111 8 1000 1000 9 1001 1001 10 1010 0001 0000 11 1100 0001 0001

4. Excess-3 Exess-3 is also known as self complementing or reflective code. (Excess-3)=BCD+3. DIGIT BCD EXCESS-3 0000 0011 1 0001 0100 2 0010 1101 3 0011 0110 4 0100 0111 5 0101 1000 6 0110 1001 7 0111 1010 8 1000 1011 9 1001 1100

5. EXCESS-3 TO BCD We know that, excess-3 code begins with the binary 0011(decimal 3) and it will continue up to binary 1100(decimal 12) where I get the output binary 1001(decimal 9) for input binary 1100(decimal 12). So I need 4 variables as inputs and 4 variables as outputs. With 4 variables I can represent 16 binary values from 0000 to 1111. Since I do not use 0, 1, 2, 13, 14, 15 as inputs, when I simplify the output function I use those terms as don’t care conditions.

6. Observation E3 E2 E1 E0 B3 B2 B1 B0 x x x x 1 x x x x 1 x x x x 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X x x x 1 1 1 x x x x 1 1 1 1 x x x x

7. B3=m(11,12)+d(0,1,2,13,14,15) =>B3=(E3.E1.E0)+(E3.E2). B2=m(7,8,9,10)+ d(0,1,2,13,14,15). =>B2=(E2’.E1’)+(E2’.E0’)+(E2.E1.E0). B1=m(5,6,9,10)+ d(0,1,2,13,14,15). =>B1=(E1’.E0)+(E1.E0’). B0=m(4,6,8,10,12)+ d(0,1,2,13,14,15). => B0=(E0’).

8. Circuit