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4 - 1 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

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4 - 2 Alphanumeric Character codes Character 6-bit internal code ASCII code 8-bit EBCDIC A B C D E F G H I J ………… …………………

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4 - 3 ASCII 7-bit Codes

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4 - 4 Binary Codes for Decimal Numbers Weighted codes: 8421, 6311, Excess-3Non-weighted codes: 2-out-of-5, Gray

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4 - 5 Binary Codes for Decimal Numbers (cont.) BCD - Convert decimal numbers to binary code, digit by digit (at least bits required) code: code: (for each decimal digit) By looking up the previous table

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4 - 6 The Meaning of Data 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: = 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 C I 9096 ???Meaningless, why???

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4 - 7 Boolean Algebra George Boole ( ) 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

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4 - 8 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

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4 - 9 Basic Operations 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: NOT (compliment or invert) AND OR 1´ or 1 X ´ or X X Y X + Y 1 + X C = X´ inversion symbol or “bubble

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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 0 or 1 0 & 5V; -12V & 0V, etc. if X = 0 C = 1 if X = 1 C = 0 Truth Table X C B

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

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