Binary Codes Computers and other digital systems "work" with binary numbers. I/P & O/P is usually done using decimal numbers, alphabetics, special symbols. Some way of representing alphanumerics with binary numbers is required. These representations are called codes. Many codes are possible, and a few standard codes are used, such as: ASCII - American Standard Code for Information Interchange   EBCDIC - Extended Binary Coded Decimal Interchange Code    BCD - Binary Coded Decimal. For numbers only.   Hardware and/or software is required to convert coded numbers into binary numbers before any arithmetic operations can take place. 7-bit System Used in Big Mainframe Systems

Alphanumeric Character codes Character 6-bit internal code ASCII code 8-bit EBCDIC A 010 001 100 0001 1100 0001 B 010 010 100 0010 1100 0010 C 010 011 100 0011 1100 0011 D 010 100 100 0100 1100 0100 E 010 101 100 0101 1100 0101 F 010 110 100 0110 1100 0110 G 010 111 100 0111 1100 0111 H 011 000 100 1000 1100 1000 I 011 001 100 1001 1100 1001 J 100 001 100 1010 1101 0001 ………… …………………

ASCII 7-bit Codes

Binary Codes for Decimal Numbers Weighted codes: 8421, 6311, Excess-3 Non-weighted codes: 2-out-of-5, Gray

Binary Codes for Decimal Numbers (cont.) BCD - Convert decimal numbers to binary code, digit by digit (at least bits required).   8421 code: 95.16 6311 code: 925 4 (for each decimal digit) 1001 0101 . 0001 0110 9 5 1 6 1100 0011 0111 By looking up the previous table

The Meaning of Data 5012110 C I 9096 ??? Meaningless, why??? e.g.: Consider the following 16-cell register If one assumes that the content of the register represents a binary integer, the decimal number is: 1100001111001001 =   If one assumes an 8-bit EBCDIC code, the two characters are: In excess-3 code:    In BCD code: The same bit configuration may be interpreted differently for different types of elements of information. The computer must be programmed to process this information according to the type of information stored. 5012110 C I 9096 ??? Meaningless, why???

Boolean Algebra George Boole (1815-1864) applied a set of symbols to logical operations. Digital electronics applies his set theory and logic to (binary) switching networks. Binary number system is used to represent the two possible states of our systems.  The symbols 0 & 1 are used to represent:   True or False   Flow or No Flow   Open or Closed   Voltage1 or Voltage2   etc. word statements currents, fluids switches, doors, etc. anything with 2 states

Boolean Algebra Deals with manipulation of Variables & Constants Boolean Variables, such as X, Y, Z, A, B, C, etc. can have "values" of either 0 or 1.  0 & 1 are constants & are symbols only, representing two different states of a quantity. i.e. F or T Low voltage or high voltage, usually written L or H Flow or not flow e.g. 0V  logical 0 +5V  logical 1 or 0V  1 +5V  0 + ve logic - ve logic

NOT (compliment or invert) AND OR Basic Operations NOT (compliment or invert) AND OR Only 3 e.g. Not 1 is written as:   Not :   X and Y :   X or Y :   1 or X :  If the variables represent voltages of the I/P or O/P of a switching network, we symbolically represent these operations by: NOT If O/P is called C, we write: 1´ or 1 X ´ or X X • Y X + Y 1 + X inversion symbol or “bubble C = X´

Boolean Operations (cont.) AND   OR where values for X, A, B, C are . They actually correspond to two different voltage levels when realized electronically. e.g. Characteristics of an Inverter B 0 or 1 0 & 5V; -12V & 0V, etc. Truth Table X C 0 1 1 0 if X = 0 C = 1 if X = 1 C = 0

Boolean Operations (cont.) AND gate A B C A B C = A ● B 0 0 0 0 1 0 0 0 1 1 1 Logical Multiplication OR gate A B C A B C = A + B 1 1 Logical Addition 1 Also called Inclusive OR 1 1