bcd to excess 3 code conversion

In this article we are going to discuss about bcd to excess 3 code conversion. Before we start, make sure you have a clear concept of number system and decimal to binary conversion.

Unlike other conversions BCD to excess 3 code conversion is super easy. BCD can be converted to excess 3 code by adding number 3 to its decimal value. Suppose we need to convert 1 ( 0001 ) to its excess 3 code. Adding decimals, 1 + 3 = 4. So access 3 code for 1 is 4 ( 0100 ).

BCD to excess 3 code conversion

The code conversions from 1 to 15 is shown in the table below.

D	BCD				Excess 3 code				E
	A	B	C	D	W	X	Y	Z
0	0	0	0	0	0	0	1	1	3
1	0	0	0	1	0	1	0	0	4
2	0	0	1	0	0	1	0	1	5
3	0	0	1	1	0	1	1	0	6
4	0	1	0	0	0	1	1	1	7
5	0	1	0	1	1	0	0	0	8
6	0	1	1	0	1	0	0	1	9
7	0	1	1	1	1	0	1	0	10
8	1	0	0	0	1	0	1	1	11
9	1	0	0	1	1	1	0	0	12
10	Don’t Care Condition
11
12
13
14
15

Here D is decimal number, A, B, C & D are BCD, W, X, Y & Z are excess 3 code of BCD & E is equal to Decimal + 3. The binary coded decimal of E is excess 3 code.

Output equations

The output will be written only where logic 1 is obtained in excess 3 code. Don’t care ( d ) will be considered with all. The output can be written as –

W = Σ m ( 5, 6, 7, 8, 9 ) + d ( 10, 11, 12, 13, 14, 15 )

X = Σ m ( 1, 2, 3, 4, 9 ) + d ( 10, 11, 12, 13, 14, 15 )

Y = Σ m ( 0, 3, 4, 7, 8 ) + d ( 10, 11, 12, 13, 14, 15 )

Z = Σ m ( 0, 2, 4, 6, 8 ) + d ( 10, 11, 12, 13, 14, 15 )

K Map for W

Output equation

Y ( W ) = A + B ( C + D )

K Map for X

Output equation

Y ( X ) = A’B’ ( C + D ) + BC’D’ + AD

K Map for Y

Output equation

Y ( Y ) = C’D’ + CD

K Map for Z

Output equation

Y ( Z ) = C’D’ + CD’ = D’ ( C’ + C ) = D’

Example

Q. Convert BCD ( 0100 ) to excess 3 code.

– we know, decimal of BCD ( 0100 ) is 4. So 4 + 3 = 7 ( 0111 ).

So excess 3 code of BCD ( 0100 ) is ( 0111 ).

Excess 3 code to BCD

The process of converting excess 3 code back to BCD is just opposite. Here we subtract 3 from the excess 3 code to get the Binary Coded Decimal.

The table below shows excess 3 code and their BCD.

D	Excess 3 Code				BCD				E
	W	X	Y	Z	A	B	C	D
0	0	0	0	0	X	X	X	X
1	0	0	0	1	X	X	X	X
2	0	0	1	0	X	X	X	X
3	0	0	1	1	0	0	0	0	0
4	0	1	0	0	0	0	0	1	1
5	0	1	0	1	0	0	1	0	2
6	0	1	1	0	0	0	1	1	3
7	0	1	1	1	0	1	0	0	4
8	1	0	0	0	0	1	0	1	5
9	1	0	0	1	0	1	1	0	6
10	1	0	1	0	0	1	1	1	7
11	1	0	1	1	1	0	0	0	8
12	1	1	0	0	1	0	0	1	9
13	1	1	0	1	X	X	X	X
14	1	1	1	0	X	X	X	X
15	1	1	1	1	X	X	X	X

Here D is the decimal number, W, X, Y & Z are the excess 3 code of the decimal numbers. A, B, C & D are Binary Coded Decimals. E is equal to decimal ( D ) – 3, that starts from 3 – 3 = 0.

Example

Convert excess 3 code ( 0110 ) to BCD.

– We know, according to table given above.

Decimal number of excess 3 code ( 0110 ) is 6.

So 6 – 3 = 3 ( 0011 ).

So BCD of excess 3 code ( 0110 ) is ( 0011 )

Author

Akash Sharma

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