Number Systems

By : Ms. Kalpani ManatungaGCE (A/L) ICT Training for Teachers

Representation of NumbersGCE (A/L) ICT Training for Teachers

Integer + & - whole numbers4251 -582

Real All numbers including everything between integers0.23, 0, 5, -2.3,

Least significant bitMost significant bit

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Fixed Point Representation12.548

Floating Point RepresentationScientific Notation12.054 1.2054 * 101Computer Notation12.65 0.1265*102

Floating Point NumbersGCE (A/L) ICT Training for Teachers

Mantissa

15.23 * 10 4Radix /baseExponent

IEEE 754 32bit Floating Point RepresentationGCE (A/L) ICT Training for Teachers

Data Representation in ComputersGCE (A/L) ICT Training for Teachers

BCD (Binary Coded Decimal)

4 bit code for numeric values only9 1001

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ASCII (American Standard Code for Information Interchange)7 bit code for all 128 charactersA=1000001

EBCDIC (Extended BCD Interchange Code)8 bit ASCII

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ASCII (American Standard Code for Information Interchange)7 bit code for all 128 characters

A =1000001 65

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Unicode provides a unique number for every character, no matter what the platform, no matter what the program, no matter what the language.Fundamentally, computers just deal with numbers. They store letters and other characters by assigning a number for each one. 8, 16 or 32 bits per character

Binary AdditionGCE (A/L) ICT Training for Teachers

Rules of Binary Addition0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 0, and carry 1 to the next more significant bit

Try out these additions:00011010 + 00001100 = ?00010011 + 00111110 = ?

Binary SubtractionGCE (A/L) ICT Training for Teachers

Rules of Binary Subtraction0 - 0 = 0 0 - 1 = 1, and borrow 1 from the next more significant bit 1 - 0 = 1 1 - 1 = 0

Try out these subtractions:00100101 - 00010001 = ?00110011 - 00010110 = ?

1s & 2s ComplementsGCE (A/L) ICT Training for Teachers

Store the integer -70 in a byte using the two's complement notation.

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