Number System (1A) Young Won Lim 7/7/10

Transcription

1 Number System (A) 7/7/

2 Copyrigt (c) 9-6 Young W. Lim. Permission is granted to copy, distribute and/or modify tis document under te terms of te GNU ree Documentation License, Version. or any later version publised by te ree Software oundation; wit no Invariant Sections, no ront-cover Texts, and no Back-Cover Texts. A copy of te license is included in te section entitled "GNU ree Documentation License". Please send corrections (or suggestions) to youngwlim@hotmail.com. Tis document was produced by using OpenOffice/LibreOffice. 7/7/

3 Coin Tossing H H T H H T T H H H T T H T T H H H T H T T T H H T T T H T x x x =.Numbers

4 Coin Tossing and Binary Number x x x =.Numbers

5 Radix Number Systems Decimal Binary d d d d b b b b Octal Hexadecimal o o o o h h h h.numbers

6 Conversion to decimal numbers Decimal d + d + d + d Binary b + b + b + b Octal o 8 + o 8 + o 8 + o 8 Hexadecimal h 6 + h 6 + h 6 + h 6.Numbers 6

7 Number Systems [..] radix= radix= radix=6 radix= A B C D E 6 7 Decimal Binary Hexadecimal Octal.Numbers 7

8 Binary and Hexadecimal Numbers 6 radix= radix=6 Binary x + ( )x 8 9 A 6 x B C D E Binary Hexadecimal Hexadecimal Decimal 6 6 x6 + = 8.Numbers 8

9 Bit Patterns radix= radix=6 radix= A B C D E 6 7 Bit patterns stored in a computer memory system Unsigned Signed Each bit pattern can represent either unsigned or signed numbers Binary HEX OCT.Numbers 9

10 Signed and Unsigned Numbers radix= radix=6 radix=8 Bit patterns in a computer radix= radix= A B C Can represent either unsigned or signed numbers 6 D E 6 7 Binary HEX OCT Unsigned Signed.Numbers

11 's Complement signed numbers Bit patterns in a computer Can represent either positive or negative numbers Binary - 's complement.numbers

12 's Complement signed numbers Bit patterns in a computer Binary Can represent either positive or negative numbers The largest negative number : - 's complement Numbers

13 s and 's complement signed numbers 's complement Binary 's complement.numbers

14 .Numbers Compute 's Complement (+ ) 's complement 's complement Add

15 .Numbers Compute 's Complement ( +) 's complement 's complement Add

16 Types of Integer Numbers byte : char bytes: short bytes: int Numbers 6

17 Unsigned Integer Ranges Byte 7 Bytes 6 7 Bytes Numbers 7

18 Signed Integer Ranges Byte 7 Bytes 6 7 Bytes Numbers 8

19 Integer Ranges Byte 7 Bytes 6 7 Bytes unsigned char unsigned short unsigned int [, +( 8 )] [, +( 6 )] [, +( )] (signed) char (signed) short (signed) int [, +( 7 )] [, +( )] [, +( )] [ 7, ] [, ] [, ].Numbers 9

20 Byte Unsigned Integer Example Hexadecimal D 8 6 x x6 6 + x6 + 6x6 + x6 + x6 + 8x6 + = 66.Numbers

21 Byte Signed Integer positive number D x x6 6 + x6 + 6x6 + x6 +x6 + 8x6 + = + 66.Numbers

22 Byte Signed Integer negative number s complement 8 B 9 7 D 7 6 ( x x6 6 + x6 + 9x6 + x6 + x6 + 7x6 + ) = 687.Numbers

23 Sign Extension () -bit Signed Number 8-bit Signed Number 6-bit Signed Number (+) (+) (+) () () () Numbers

24 Sign Extension () x6 + x6 + x6 + x6 + D D D ( ) ( x6 + ) ( x6 + x6 + x6 + ).Numbers

25 Sign Extension () A B C D E Hexadecimal Binary.Numbers

26 loating Point Number ormat float Sign (-bit) Exponent (8-bits) raction (-bits) Bytes double Sign (-bit) Exponent (-bits) raction (-bits) 8 Bytes

27 Signed and Unsigned Number Examples unsigned char u; = + (signed) char i; s complement = +.Numbers 7

28 Conversion Specifier unsigned int u; %d %u (signed) (unsigned) (signed) int i; %d - (signed) %u (unsigned).numbers 8

29 Conversion Specifier unsigned int u; 8 = + + %d %u (signed) (unsigned) (signed) int i; + %d %u (signed) (unsigned).numbers 9

30 Conversion Specifier unsigned char u; 8 = + + (signed) char i; +.Numbers

31 Single Precision : float : positive, : negative exponent Excess +7 (must be subtracted) 7 = 8 Implicit fraction

32 Single Precision : float

33 Double Precision : double : positive, : negative exponent Excess + (must be subtracted) = Implicit fraction

34 Double Precision : double

35 References [] Essential C, Nick Parlante [] Efficient C Programming, Mark A. Weiss [] C A Reference Manual, Samuel P. Harbison & Guy L. Steele Jr. [] C Language Express, I. K. Chun 7/7/