# 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 CareCondition 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

Half adder and full adder is a part of combinational circuits. Combinational circuits are those whose output characteristics depends on their input levels at a particular time.

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