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.
DIGI
T
BINARY BCD
0 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
0 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
0 0 0 0 x x x x
0 0 0 1 x x x x
0 0 1 0 x x x x
0 0 1 1 0 0 0 0
0 1 0 0 0 0 0 1
0 1 0 1 0 0 1 0
0 1 1 0 0 0 1 1
0 1 1 1 0 1 0 0
1 0 0 0 0 1 0 1
1 0 0 1 0 1 1 0
1 0 1 0 0 1 1 1
1 0 1 1 1 0 0 0
1 1 0 0 1 0 0 1
1 1 0 1 X x x x
1 1 1 0 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