Computer Codes:

The second category of codes are those codes which cannot be represented by any analytical relation, hence these codes are also called as non-analytical code.Non-Analytical code. These are the following codes:

Non-Weighted Codes:

Excess-3 Codes, Gray Codes, BCD greater than 4-bits

Self Complementing codes:

2421, 5211, Excess-3 (XS-3)

Sequential Codes:

8421 and XS-3

Cyclic Code:

Gray Code

Reflecting Code:

Gray Code

Error Detection and Correcting Code:

Parity, Hamming Code

Gray Code

This code also known as a unit distance code. This code is best suited as a shat position encoder. Going from any one position to next position, there is only one bit change in the code. The pattern formed by the gray code is the mirror image, so the code is also called as reflected code. Figure shows the formation of gray code from 1-bit to 2-bits and from 2-bit to 3-bit.

 

Binary coded decimal(BCD) :

This code is an extension of decimal code. This code make use of 4-bit binary code for decimal digit 0 through 9. As with 4-bit, we can have 16 combinations, but the valid decimal digit symbols are from 0 to 9, code 1010 to 1111 are invalid code in BCD.

To encode in BCD, 4-bit code of each decimal digit is written to form a valid binary equivalent

Examples

Decimal —–>	9	10	128	458	89
BCD   —–>	1001	0001 0000	0001 0010  1000	0100 0101 1000	1000 1001

 

Self Complementing Codes

Excess-3 (XS-3) code:

An XS-3 code is obtained by adding 3 with the equivalent decimal of a binary number and again converting it into binary number.

Procedure:

• Convert a binary to its decimal equivalent: e.g. 1001 = 9₁₀
• Add 3 to the decimal digit: in XS-3, add 3, so 9+3=12.
• Convert the decimal back to binary : write the binary Code of 12, which is code of 9 in XS-3

 

Binary	Decimal	+3	XS-3
0000	0	0+3 =3	0011
0001	1	1+3=4	0100
0010	2	2+3=5	0101
0011	3	3+3=6	0110
0100	4	4+3=7	0111
0101	5	5+3=8	1000
0110	6	6+3=9	1001
0111	7	7+3=10	1010
1000	8	8+3=11	1011
1001	9	9+3=12	1100

Conversion from bigger decimal numbers to XS-3 is also simple:

• To each decimal digit, add 3
• Write equivalent binary code for each number so formed.

Example:

Decimal	4 810	92010	7310
Add 3 to each digit	(4+3) (8+3) 7           11	(9+3)  (2+3)  (0+3) 12       5        3
XS-3 Code	0111   1011	1100    0101  0011

 

Advantage:

The primary advantage of XS-3 coding over non-biased coding is that a decimal number can be nines’ complemented (for subtraction) as easily as a binary number can be ones’ complemented; just invert all bits.

Self Complementing:

Excess-3(XS-3) code

Just complement the bits to get the 9’s complement

Decimal	6	9	1
XS-3 Code	1001	1100	0100
Complement Bits	0110	0011	1011
9’s complement “(XS-3) – 3”	3	0	8
Summary ->	9’s complement of 6 is 3	9’s complement of    9 is 0	9’s complement of 1 is 8

 

2421BCD:

The weight of the bits is 2, 4, 2, 1 and the numbers formed are:

	2	4	2	1
0	0	0	0	0
1	0	0	0	1
2	0	0	1	0
3	0	0	1	1
4	0	1	0	0
5	0	1	0	1
6	0	1	1	0
7	0	1	1	1
8	1	1	1	0
9	1	1	1	1

5421 Binary Coded Decimal Code

	5	4	2	1
0	0	0	0	0
1	0	0	0	1
2	0	0	1	0
3	0	0	1	1
4	0	1	0	0
5	0	1	0	1
6	0	1	1	0
7	0	1	1	1
8	1	0	1	1
9	1	1	0	0
10	1	1	0	1
11	1	1	1	0
12	1	1	1	1

 Quiz

1. The BCD equivalent of decimal 648₁₀ =
2. XS-3 equivalent of BCD 89₁₀   =
3. What is 2421 equivalent of 8 =
4. What is the gray code equivalent of decimal 3………..
5. Convert 1010 into gray code =………..