CODING
Binary code
• Digital data is represented, stored and transmitted as group of binary
bits.
• This group is called binary code.
• The binary code can be used for represent the number as well as alpha
numeric letters.
Classification of
binary code
Binary code
Weighted code
Binary
Ex: 0s1
Non weighted code
Reflective code
Sequential code
Error detecting and
correcting code
•Example:
Gray
Excess-3
Five bit BCD
•Example:
5211
2421
Excess-3
•Example:
8421
Excess-3
•Example:
Hamming
Parity
• BCD
Ex:
8421
2421
5211
4221
Binary code decimal
(BCD)
• We know that decimal, octal, hexadecimal can be represented
by binary digit.
• Not only numbers but letters and other symbols can be
represented by 1s 0s.
• Combination of binary digits that represent all these things are
called digital codes.
Binary code decimal
(BCD)
8421 (BCD)
Decimal
0000
0
0001
1
0010
2
0011
3
0100
4
0101
5
0110
6
0111
7
1000
8
1001
9
Gray code
• It is called cyclic or reflected code.
• In this code each code group does not differ from its
neighbour in more than one bit.
• This code is used for input and output devices in
digital system.
Table of gray code
Decimal number
Gray code
0
0 0 0 0
1
0 0 0 1
2
0 0 1 1
3
0 0 1 0
4
0 1 1 0
5
0 1 1 1
6
0 1 0 1
7
0 1 0 0
8
1 1 0 0
9
1 1 0 1
10
1 1 1 1
11
1 1 1 0
12
1 0 1 0
Conversion from
binary to gray code
Method:
•
Write down binary form of the given decimal number.
•
Write MSB as such.
•
Then add the binary digit from left to right at the adjacent
position.
•
Discard carry if any.
•
Write the digit which comes after addition.
Conversion from
binary to gray code
• Example:
Convert 15 into gray code.
Solution: (15)10 = (1111)2
We have to convert (1111)2 into gray code
Left most bit
1
1
+
1
0
+
1
0
+
1
0
Hence the resultant gray code is 1000 for 15.
Example
–
Convert (111011)2 into gray code.
Solution:
Left most bit
1
1
1.
2.
3.
+
1
0
+
1
0
+
+
+
0
1
1
1
1
0
Write the left most bit as such.
Then add the binary digit from left to right at the adjacent position.
Write the digit which comes after addition.
Hence the grey code of (111011)2 is 100110.
Conversion from grey
code to binary code
•
Method:
1.
Write the given grey code.
2.
Write the left most bit as such.
3.
Add this bit to the second left most bit, write the result,
discard carry.
4.
Add this result to the next left most bit diagonally.
Conversion from grey
code to binary code
• Example:
Convert the following grey code into binary code from (1 0 0 0).
Solution:
We have Left most bit
1
0
+
1
1
+
0
+
1
Hence the corresponding binary number us (1111)2.
0
1