How do you convert bcd into Gray code?

Answer 1

Hexidecimal (Base 16)

0000 = 0

0001 = 1

0010 = 2

0011 = 3

0100 = 4

0101 = 5

0110 = 6

0111 = 7

1000 = 8

1001 = 9

1010 = A

1011 = B

1100 = C

1101 = D

1110 = E

1111 = F

BCD (Binary coded decimal is just 0 through 9 above)

Answer 2

Binary coded decimal (BCD) requires a minimum of 4 bits to represent all possible digits from 0 to 9. There are ten possible configurations for a BCD with the following corresponding Gray codes, which also require a minimum of 4 bits:

Digit : BCD : Gray

0 : 0000 : 0000

1 : 0001 : 0001

2 : 0010 : 0011

3 : 0011 : 0010

4 : 0100 : 0110

5 : 0101 : 0111

6 : 0110 : 0101

7 : 0111 : 0100

8 : 1000 : 1100

9 : 1001 : 1101

To convert from BCD to Gray, you must be familiar with the XOR binary logic gate. This gate has two inputs (hence it is a binary gate) and one output. When either input is true, but not both, the output is true. The truth table for all possible inputs p and q can therefore be summarised as follows:

p q output

0 0 0

0 1 1

1 0 1

1 1 0

To implement a conversion from BCD to Gray, we use the following algorithm:

Step 1: Fix the MSB (most-significant bit). This bit is always the same for both codes, regardless of length. If there are no more bits, we're done, otherwise proceed to step 2.

Step 2: XOR the first and second BCD bit to fix the next Gray bit.

Step 3: Disregard the first BCD bit.

Step 4. If there are two or more BCD bits remaining, go to step 2. Otherwise we're done.

For example, to convert BCD 0101 we proceed as follows:

(Fix MSB = 0)101

(0 XOR 1 = 1)01

(1 XOR 0 = 1)1

(0 XOR 1 = 1)

Thus BCD 0101 is Gray 0111. Consulting the table above will confirm this to be true.

Implementing this algorithm electronically is beyond the scope and capability of this wiki. However, see related links, below, for further information.