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Bits, Nybbles, Bytes, numbers and characters

Bits, Nybbles, Bytes, numbers and characters. Brian Mapes MPO581 Jan 24, 2011 from googling and poaching. Data Types. bit - a 0 or 1. Can represent 2 unique values byte - 8 bits. 256 values -128 to 128 unsigned byte - 8 bits 0 to 256 character – an alphabet-mapped byte

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Bits, Nybbles, Bytes, numbers and characters

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  1. Bits, Nybbles, Bytes, numbers and characters Brian Mapes MPO581 Jan 24, 2011 from googling and poaching

  2. Data Types • bit - a 0 or 1. Can represent 2 unique values • byte - 8 bits. 256 values -128 to 128 • unsigned byte - 8 bits 0 to 256 • character – an alphabet-mapped byte • short int - 16 bits -32767 to 32767 • long int – 32 bits 4,294,967,296 values • float - 32 bits coded: mantissa,exp • double - 64 bits coded • word – machine dependent. 32 or 64 bits

  3. Binary Equivalents of Decimal Numbers DecimalBinary (LR) Binary (R L) 0 0000 0000 1 0001 1000 2 0010 0100 3 0011 1100 4 0100 etc. 5 0101 6 0100 7 01118 1000 Is “most significant bit” (MSB) at “right” or “left”? (right and left are arbitraryin computer chip memory space)

  4. Powers of 2 DecimalDecimal 20 1 28 256 21 2 29 512 22 4 210 1024 23 8 211 2048 24 16 212 4096 25 32 213 8192 26 64 214 16384 27 128 215 32768

  5. Decimal (base 10) numbers • A decimal number can be represented as the sum of powers of 10 (the base) with coefficients in the base 10 alphabet (0 - 9) For example: 2485 = 2000 + 400 + 80 + 5 2485 = 2 * 1000 + 4 * 100 + 8 * 10 + 5 * 1 2485 = 2 * 103 + 4 * 102 + 8 * 101 + 5 * 100 Same principle can be applied in binary...

  6. Hexadecimal Numbers (nybbles or half-bytes) • 4 bits  Base-16 number system • Uses digits 0 - 9 and letters A - F • One hexadecimal digit can express values from 0 to 15 • For example: C represents 12 • (Not important for us - Used in memory addressing, sometimes wifi passwords,...)

  7. Hexadecimal - Binary Equivalents Hex Binary Hex Binary 0 0000 8 1000 1 0001 9 1001 2 0010 A 1010 3 0011 B 1011 4 0100 C 1100 5 0101 D 1101 6 0110 E 1110 7 0111 F 1111

  8. Characters and strings • Characters and Strings • EBCDIC, Extended Binary Coded Decimal Interchange Code • Used by IBM in mainframes (360 architecture and descendants). • Earliest system • ASCII, American Standard Code for Information Interchange. • Most common system • Unicode, http://www.unicode.org • New international standard • Variable length encoding scheme with either 8- or 16-bit minimum • “a unique number for every character, no matter what the platform, no matter what the program, no matter what the language.”

  9. The Unicode Character Set • Each character stored as 16-bits • Maximum number of characters that can be represented: 65,536 (216) • ASCII character set (used by many programming languages) stores each character as 7 bits (maximum number of characters is 128). • For compatibility, first 128 characters of Unicode set represent the ASCII characters

  10. Some Unicode Characters Unicode CharacterDecimal Value * 42 1 49 2 50 A 65 B 66 a 97 b 98 } 125

  11. Bytes as the “element” of data • Memory: Can be viewed as an array of storage elements. • The index of each element is called the address. • Each element holds the same number of bits. • How many bits per element? 8, 16, 32, 64? • 8 (Byte) is typical • Words are about the processor: how many bytes are loaded into a register and processed at once? • 32-bit word common, 64-bit  faster double math 8 bits = 1 byte 16 bits 32 bits 64 bits 0 0 0 0 1 1 1 1 2 2 2 2 ... ... ... ... n-1 n-1 n-1 n-1

  12. Single precision

  13. Charles Babbage 1791-1871Lucasian Professor of Mathematics, Cambridge University, 1827-1839 CS152-Spring’09

  14. The first programmer Ada Byron aka “Lady Lovelace” 1815-52 Ada’s tutor was Babbage himself! CS152-Spring’09

  15. Babbage’s Influence • Babbage’s ideas had great influence later primarily because of • Luigi Menabrea, who published notes of Babbage’s lectures in Italy • Lady Lovelace, who translated Menabrea’s notes in English and thoroughly expanded them. “... Analytic Engine weaves algebraic patterns....” • In the early twentieth century - the focus shifted to analog computers but • Harvard Mark I built in 1944 is very close in spirit to the Analytic Engine. CS152-Spring’09

  16. Application Programs High-Level Languages Machine independent High-Level Language Machine specific Low-Level Language Assembly Language Machine Language Hardware A Hierarchy of Languages

  17. Bit depths in color • 16 bits per pixel (high color) • 5 bits for red, 5/6 bits for green, 5 bits for blue • potential of 32 reds, 32/64 green, 32 blues • total colors: 65536 • 32 bits per pixel (true color) • 8 bits for red, green, blue, and alpha • potential for 256 reds, greens, and blues • total colors: 16777216 (more than the eye can distinguish)

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