Digital Electronics and Logic Design (DELD) Module 1 Note for KTU S4 EEE Students
Number Systems and Codes : Binary, Octal and hexadecimal conversions- ASCII code, Excess -3 code, Gray code, Error detection and correction - Parity generators and checkers – Fixed point and floating point arithmetic. Binary addition and subtraction, unsigned and signed numbers, 1's complement and 2’s complement arithmetic.
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Sample topic :-
Binary codes:- BCD, GRAY, EBCDIC, ASCII
· It is the symbolic representation of discrete information which may be represented in the form of numeric, alphabets & special characters.
· In Digital Electronics, the binary digits 0 & 1 are used to represent these symbols & are arranged according to the rules of specific code.
· Infect, a binary code is a group of n-bits that can represent distinct symbols.
· The interpretation of the binary information is possible only if the code in which this information is available is known.
Different codes
1. Natural BCD Code
In this code, decimal 0 through 9 are represented by their natural binary equivalents using four bits and each decimal digit is represented by this four bit code individually. This code is also known as 8-4-2-1 code where 8, 4, 2, & 1 are the weights of the four bits of the binary code of each decimal digit to the straight binary system.
2. EXCESS-3 Codes
This is another form of BCD code, in which each decimal is coded into a 4-bit binary code. The code for each decimal digit is obtained by adding decimal 3 to the natural BCD code of the digit. For ex- decimal 2 is coded as 0010+0011=0101 in Excess-3 code
3. Gray Code
It is a very useful code in which a decimal number is represented in binary form in such a way so that each gray code number differs from preceding & the succeeding number by a single bit. For ex- the gray code for decimal number 5 is 0111 & for 6 is 0101. These two codes differ by only one bit position (third from left). This code is used extensively for the shaft encoders because of this property.
Classification of Codes
1. Weighted & Non-weighted Codes
The main characteristic of weighted code is that each binary digit is assigned a specific weight. The common example of weighted code is BCD code or 8421 code in which the weights of different bits are 1, 2, 4 & 8
Non-Weighted Code: These don’t follow the principle of positional weighting system i.e. each position within the number doesn’t follow or have any fixed weight. For ex- Excess-3, Gray code.
2. Self-Complimentary & Sequential Codes
A code is said to be self-complementary if the code for 9’s
complement of N i.e. 9-N can be obtained by interchanging all 0sand 1s.
· Decimal 9 is the complement of code for 0, 8 for 1, 7 for 2 and soon.
· For a code to be self complementing, the sum of all its weights must be 9. digit.8421 and 5421 codes are not self-complementing codes whereas 5211,2421,3321, 4321 are self complementing.
· In general, a code is self-complementary if we produce a code by taking the
first complement of the digit which is same as 9’s complement of the number.
Sequential Code: These are those codes in which each succeeding code is 1 binary number greater than the preceding code. This property is used for mathematical manipulation of data. For ex:- BCD And Excess-3 Code.
3. Alphanumeric codes
· Apart from numeric data, a computer system may process some alphanumeric data just like the employees’ names, address as well as some special characters. An Alphanumeric data generally consist of sequence of characters where a character is any one of the following:-
· Letters or alphabets
· Digits 0-9
· Special characters(+,-,π)
· In the computer system, each character is stored in some code form depending upon the coding scheme. The character may take 6, 7, or 8 bits. There are number of codes which are used for some specific application i.e. ASCII Code, EBCDIC Code, UNIT Code, etc.
4. Error detection & Error correction Codes