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Unformatted text preview: Chapter 2  Data Types BYU CS/ECEn Chapter 2  Data Types 2 Topics to Cover… n Binary Digital System n Data Types n Conversions n Binary Arithmetic n Overflow n Fixed Point n Floating Point n Hexadecimal Numbers n ASCII Characters BYU CS/ECEn Chapter 2  Data Types 3 What are Decimal Numbers? n “Decimal” means that we have ten digits to use in our representation of numbers n Symbols 0 through 9 n Positional notation n Most widely used by modern civilizations n What is 3,546? n 3 thousands + 5 hundreds + 4 tens + 6 ones . n 3,54610 = 3103 + 5102 + 4101 + 6100 n How about negative numbers? n Need additional symbol(s) Digital Binary System BYU CS/ECEn Chapter 2  Data Types 4 What are Binary Numbers? n “Binary” means that we have two digits to use in our representation of numbers n Symbols 0 and 1 n Positional notation n More adaptable for computers n What is the decimal value of binary 1011? n 1 eights + fours + 1 twos + 1 ones n 10112 = 123 + 022 + 121 + 120 n How about negative numbers? n We don’t want to add additional symbols n So… Digital Binary System BYU CS/ECEn Chapter 2  Data Types 5 Binary Digital System n What is a Binary Digital System? n Binary (base 2) means there are two states, 0 and 1. n Digital means there are a finite number of symbols. n Basic unit of information is the binary digit , or bit . n How are bits represented? n Voltages n Residual magnetism n Light n Polarization n What about more than two states? n A collection of 2 bits has 4 possible states: 00, 01, 10, 11 n A collection of 3 bits has 8 possible states: 000, 001, 010, 011, 100, 101, 110, 111 n A collection of n bits has 2n possible states. Digital Binary System BYU CS/ECEn Chapter 2  Data Types 6 Electronic Representation of a Bit n Computers rely only on approximate physical values. n A logical ‘1’ is a relatively high voltage (2.4V  5V). n A logical ‘0’ is a relatively low voltage (0V – 0.5V). n Analog processing relies on exact physical values which are affected by temperature, age, etc. n Analog values are never quite the same. n Each time you play a vinyl album, it will sound a bit different. Digital Binary System n Bits rely on approximate physical values which are not affected by age, temperature, etc. n Music that never degrades. n Pictures that never get dusty or scratched. BYU CS/ECEn Chapter 2  Data Types 7 Binary Nomenclature Digital Binary System Name (Symbol) Value Binary Byte (B) 100 20 1 byte Kilobyte (kB) 103 210 1024 bytes Megabyte (MB) 106 220 1,048,576 bytes Gigabyte (GB) 109 230 1,073,741,824 bytes Terabyte (TB) 1012 240 1,099,511,627,776 bytes Petabyte (PB) 1015 250 1,125,899,906,842,624 bytes Exabyte (EB) 1018 260 1,152,921,504,606,846,976 bytes Zettabyte (ZB) 1021 270 1,180,591,620,717,411,303,424 bytes Yotabyte (YB) 1024 280 1,208,925,819,614,629,174,706,176 bytes n By using groups of bits, we can achieve high precision....
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 Winter '09
 Binary numeral system, Positional notation, Decimal

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