# L07 - CS 61C L07 Number Representation (1) Wawrzynek Fall...

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Unformatted text preview: CS 61C L07 Number Representation (1) Wawrzynek Fall 2007 UCB 9/12/2007 John Wawrzynek (www.cs.berkeley.edu/~johnw) www-inst.eecs.berkeley.edu/~cs61c/ CS61C Machine Structures Lecture 7 Number Representation CS 61C L07 Number Representation (2) Wawrzynek Fall 2007 UCB Decimal Numbers: Base 10 Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Example: 3271 = (3x10 3 ) + (2x10 2 ) + (7x10 1 ) + (1x10 ) CS 61C L07 Number Representation (3) Wawrzynek Fall 2007 UCB Numbers: positional notation Number Base B B symbols per digit: Base 10 (Decimal): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Base 2 (Binary): 0, 1 Number representation: d 31 d 30 ... d 2 d 1 d 0 is a 32 digit number value = d 31 x B 31 + d 30 x B 30 + ... + d 2 x B 2 + d 1 x B 1 + d x B Binary: 0,1 (In binary digits called bits) 1011010 = 1x2 6 + 0x2 5 + 1x2 4 + 1x2 3 + 0x2 2 + 1x2 + 0x1 = 64 + 16 + 8 + 2 = 90 Notice that 7 digit binary number turns into a 2 digit decimal number A base that converts to binary easily? CS 61C L07 Number Representation (4) Wawrzynek Fall 2007 UCB Which base do we use? Decimal: great for humans, especially when doing arithmetic Hex: if human looking at long strings of binary numbers, its much easier to convert to hex and look 4 bits/symbol Terrible for arithmetic on paper Binary: what computers use; you will learn how computers do +,-,*,/ To a computer, numbers always binary Regardless of how number is written: 32 10 == 0x20 == 100000 2 Use subscripts ten, hex, two in book, slides when might be confusing CS 61C L07 Number Representation (5) Wawrzynek Fall 2007 UCB Hexadecimal Numbers: Base 16 Hexadecimal: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F Normal digits + 6 more from the alphabet In C, written as 0x (e.g., 0xFAB5) Conversion: Binary Hex 1 hex digit represents 16 decimal values 4 binary digits represent 16 decimal values 1 hex digit replaces 4 binary digits One hex digit is a nibble . Two is a byte Example: 1010 1100 0011 (binary) = 0x_____ ? CS 61C L07 Number Representation (6) Wawrzynek Fall 2007 UCB Decimal vs. Hexadecimal vs. Binary Examples: 1010 1100 0101 (binary) = AC5 (hex) 10111 (binary) = 0001 0111 (binary) = 17 (hex) 3F9(hex) = 11 1111 1001 (binary) How do we convert between hex and Decimal? 00 0 0000 01 1 0001 02 2 0010 03 3 0011 04 4 0100 05 5 0101 06 6 0110 07 7 0111 08 8 1000 09 9 1001 10 A 1010 11 B 1011 12 C 1100 13 D 1101 14 E 1110 15 F 1111 CS 61C L07 Number Representation (7) Wawrzynek Fall 2007 UCB What to do with representations of numbers?...
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## This note was uploaded on 04/09/2008 for the course CS 61A taught by Professor Harvey during the Spring '08 term at University of California, Berkeley.

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L07 - CS 61C L07 Number Representation (1) Wawrzynek Fall...

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