Presentation on theme: "Binary Codes Computers and other digital systems "work" with binary numbers. I/P & O/P is usually done using decimal numbers, alphabetics, special symbols."— Presentation transcript:
1 Binary CodesComputers 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 forInformation Interchange EBCDIC - Extended Binary Coded DecimalInterchange 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 SystemUsed in Big Mainframe Systems
2 Alphanumeric Character codes Character 6-bit internal code ASCII code bit EBCDICABCDEFGHIJ……………………………
5 Binary Codes for Decimal Numbers (cont.) BCD - Convert decimal numbers to binary code, digit by digit(at least bits required).8421 code:6311 code: 925(for each decimal digit)9516By looking up the previous table
6 The Meaning of Data 5012110 C I 9096 ??? Meaningless, why??? e.g.: Consider the following 16-cell registerIf 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 I9096???Meaningless, why???
7 Boolean AlgebraGeorge 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 statementscurrents, fluidsswitches, doors, etc.anything with 2 states
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 TLow voltage or high voltage, usually written L or HFlow or not flowe.g. 0V logical 0+5V logical 1or 0V 1+5V 0+ ve logic- ve logic
9 NOT (compliment or invert) AND OR Basic OperationsNOT (compliment or invert)ANDOROnly 3e.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:NOTIf O/P is called C, we write:1´ or 1X ´ or XX • YX + Y1 + Xinversion symbol or “bubbleC = X´
10 Boolean Operations (cont.) ANDORwhere values for X, A, B, C are They actually correspond to two different voltage levels when realized electronically.e.g.Characteristics ofan InverterB0 or 10 & 5V; V & 0V, etc.Truth TableX Cif X = 0 C = 1if X = 1 C = 0
11 Boolean Operations (cont.) AND gateABCABC = A ● BLogical MultiplicationOR gateABCABC = A + B11Logical Addition1Also called Inclusive OR11
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