Prerequisite
- Digital Signal
- Digital Circuits (AND, OR, NOT, NAND, NOR, EX-OR, EX-NOR)
- Number System (Decimal, Binary, Octal, Hexadecimal, Signed binary number)
- Codes
-
Codes
- When numbers, alphabets or words are represented by specific group of symbols
means they are encoded.
-The group of symbols used to encode them are called Codes.
- For example, the binary 1000001 represents,
65 in Decimal
41 in BCD code
alphabet A in ASCII code
- Examples of Codes:
1. Binary Code 5. Octal Code
2. Natural BCD Code 6. Hexadecimal Code
3. Excess-3 Code 7. Alphanumeric Codes
4. Gray Code 8. Error detecting and correcting code
Codes – Binary Code
- The digital data is represented, stored and transmitted
as group of bits. This group of bits is also called
as binary code.
- Only 0 & 1 are being used to represent binary code.
Binary Power 23 22 21 20
Binary Weight: 8 (MSB) 4 2 1(LSB)
- Binary codes can be classified into two types.
1. Weighted codes
2. Un-weighted codes
If the code has positional weights, then it is said to be weighted
code. Otherwise, it is an un-weighted code.
- Advantages: -> Binary codes are suitable for the computer
applications and digital communications.
-> Binary codes make the analysis and designing of
digital circuits if we use the binary codes.
Codes – BCD Code
- Each decimal digit is represented by a 4-bit binary number.
- BCD is a way to express each of the decimal digits with a binary code.
- In the Binary, with four bits we can represent sixteen numbers (0000 to 1111). But in BCD code only first
ten of these are used (0000 to 1001). The remaining six code combinations i.e. 1010 to 1111 are invalid in
BCD.
- For example,
(754)10 = (0111 0101 0100)BCD
(23)10 = (0010 0011)BCD
- Advantages : ->It is easy to covert from decimal to BCD and vice versa.
-Disadvantages : -> The addition and subtraction of BCD have different rules.
-> The BCD arithmetic is little more complicated.
-> BCD needs more number of bits than binary to represent the decimal number. So BCD
is less efficient than binary.
Codes – Excess-3 Code
- This code doesn’t have any weights. So, it is an un-weighted code.
- We will get the Excess 3 code of a decimal number by adding three 00110011 to the binary
equivalent of that decimal number. Hence, it is called as Excess 3 code.
- It is a self-complementing code.
- Excess-3 for (52)10 is,
5 2
0101 0010
+ 0011 + 0011
-------------- --------------
1000 0101
Excess-3 of (52)10 = 1000 0101
Codes – Gray Code
- Gray code is not weighted that means it does not depends on positional value of digit.
-This cyclic variable code that means every transition from one value to the next value involves only one bit
change i.e. Unit Distance Code.
- Binary to Gray Code conversion
For example, Gray code of (1011)2
1 0 1 1
⊕ ⊕ ⊕
1 1 1 0
Codes – Gray Code
Gray to Binary Conversion
For example,
Convert (1110) gray code into binary.
1 1 1 0
⊕ ⊕ ⊕ ⊕
1 0 1 1
Codes – Gray Code - Applications
Gray code is a non-weighted code and is a special case of unit-distance code.
1. Karnaugh map (K-maps)
Codes – Gray Code - Applications
Gray code is a non-weighted code and is a special case of unit-distance code.
Codes – Alphanumeric Codes
- Computer is a digital system and can only deal with 1’s and 0’s. So to deal with letters and
symbols they use alphanumeric codes.
- Alphanumeric codes, also called character codes, are binary codes used to represent
alphanumeric data. The codes write alphanumeric data, including letters of the alphabet,
numbers, mathematical symbols and punctuation marks, in a form that is understandable
and process able by a computer.
- American Standard-Code for Information Interchange (ASCII)
- Extended Binary Coded Decimal Interchange Code (EBCDIC)
Codes – Alphanumeric Codes
- American Standard-Code for Information Interchange (ASCII 7- bits)
- Extended Binary Coded Decimal Interchange Code (EBCDIC 8- bits)
Codes – Parity Code
Error is a condition when the output information does not match with the input information. During
transmission, digital signals suffer from noise that can introduce errors in the binary bits travelling from
one system to other. That means a 0 bit may change to 1 or a 1 bit may change to 0.
Codes – Error detecting and error correcting
Error detecting (Parity Code): Error is a condition when the output information does not match with the
input information. During transmission, digital signals suffer from noise that can introduce errors in the
binary bits travelling from one system to other. That means a 0 bit may change to 1 or a 1 bit may
change to 0.
Error correcting (Hamming Code): Hamming code is useful for both detection and correction of error
present in the received data.
