Binary Codes

Binary Codes

Binary Codes • Digital systems use signals that have two distinct values and circuit elements that have two stable states. • direct analogy among binary signals, binary circuit elements, and binary digits • A binary number of n digits, • for example, represented by n binary circuit elements, each having an output signal equivalent to 0 or 1. • Digital systems represent and manipulate – binary numbers – any other discrete elements of information

• Any discrete element of information that is distinct among a group of quantities can be represented with a binary code (i.e., a pattern of 0’s and 1’s).

Binary Codes (Cont..) • An n‐bit binary code is a group of n bits that assumes up to 2n distinct combinations of 1’s and 0’s, with each combination representing one element of the set that is being coded. • A set of four elements can be coded with two bits, with each element assigned one of the following bit combinations: 00, 01, 10, 11. • The bit combination of an n‐bit code is determined from the count in binary from 0 to 2n - 1.

Binary codes for decimal digits BCD(8421) ,Excess 3 code,84-2-1,2421

Gray Code • The output data of many physical systems are quantities that are continuous. • These data must be converted into digital form before they are applied to a digital system.

continuous Analog information

A/D Converter

Digital information

• Adv: one bit in the code group changes in going from one number to the next • Eg: 7 0111 70100 Gray code Binary code 81000 81100

Application • Application of Gray code: the normal sequence of binary numbers generated by the hardware may produce an error or ambiguity during the transition from one number to the next

Conversion

ASCII Code • Many applications of digital computers require the handling not only of numbers, but also of other characters or symbols, such as the letters of the alphabet. • American Standard Code for Information Interchange (ASCII), which uses seven bits to code 128 characters, • ASCII is a seven‐bit code, but most computers manipulate an eight‐bit quantity • as a single unit called a byte. Therefore, ASCII characters most often are stored one per byte

Error‐Detecting Code • To detect errors in data communication and processing, an eighth bit is sometimes added to the ASCII character to indicate its parity. • A parity bit is an extra bit included with a message to make the total number of 1’s either even or odd. • Consider the following two characters and their even and odd parity:

References • Digital Logic and Computer Design by Morris Mano