Bits and Bytes Topics Why bits? Tell me Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings »Instructions.

Slides:



Advertisements
Similar presentations
University of Washington CSE351 Announcements:  HW0, having fun?  Use discussion boards!  Sign up for mailing list  If you enrolled recently,
Advertisements

CSCE 212 Computer Organization Lecture 2 Data Representation.
Bits and Bytes 4/2/2008 Topics Physics, transistors, Moore’s law Why bits? Representing information as bits Binary/Hexadecimal Byte representations »numbers.
Bits and Bytes CS 213 Aug. 27, 1998 Topics Why bits? Representing information as bits –Binary/Hexadecimal –Byte representations »numbers »characters and.
Bits and Bytes January 17, 2002 Topics Why bits? Representing information as bits –Binary/Hexadecimal –Byte representations »numbers »characters and strings.
Bits, Bytes, and Integers August 29, 2007 Topics Representing information as bits Bit-level manipulations Boolean algebra Expressing in C Representations.
Bits and Bytes Topics Physics, transistors, Moore’s law Why bits? Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters.
ICS 2005 Instructor: Peter A. Dinda TA: Bin Lin Recitation 2.
Bits and Bytes January 15, 2004 Topics Why bits? Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings.
Bits and Bytes Topics Why bits? Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings »Instructions.
Fabián E. Bustamante, Spring 2007 Bits and Bytes Today Why bits? Binary/hexadecimal Byte representations Boolean algebra Expressing in C.
Codes and number systems Introduction to Computer Yung-Yu Chuang with slides by Nisan & Schocken ( ) and Harris & Harris (DDCA)
BITS, BYTES, AND INTEGERS SYSTEMS I. 22 Today: Bits, Bytes, and Integers  Representing information as bits  Bit-level manipulations  Integers  Representation:
Carnegie Mellon 1 Bryant and O’Hallaron, Computer Systems: A Programmer’s Perspective, Third Edition Bits, Bytes, and Integers MCS-284 : Computer Organization.
Carnegie Mellon 1 Bits, Bytes, and Integers Lecture, Jan. 24, 2013 These slides are from website which accompanies the book “Computer.
CS 270: Computer Organization Bits, Bytes, and Integers
Bits and Bytes Spring, 2015 Topics Why bits? Representing information as bits Binary / Hexadecimal Byte representations »Numbers »Characters and strings.
Bits and Bytes Topics Representing information as bits Bit-level manipulations Boolean algebra Expressing in C.
Lecture 3: Computation and Representation CS 2011 Fall 2014, Dr. Rozier.
University of Washington Memory, Data & Addressing The Hardware/Software Interface CSE351 Winter 2013.
Carnegie Mellon 1 Bits, Bytes, and Integers : Introduction to Computer Systems 3 rd Lectures, May 27th, 2014 Instructors: Greg Kesden.
Bits, Bytes, and Integers Topics Representing information as bits Bit-level manipulations Boolean algebra Expressing in C Representations of Integers Basic.
1 Saint Louis University Arithmetic and Bitwise Operations on Binary Data CSCI 224 / ECE 317: Computer Architecture Instructor: Prof. Jason Fritts Slides.
Bits and Bytes September 2, 2004 Topics Why bits? Representing information as bits Binary / Hexadecimal Byte representations »Numbers »Characters and strings.
– 1 – Number Systems Number of symbols = base of the system Most intuitive -- base 10 (decimal system) counting on fingertips symbols
Info stored in computer (memory) Numbers All in binaray – can be converted to octal, hex Characters ASCII – 1-byte/char Unicode – 2-byte/char Unicode-table.com/en.
Carnegie Mellon 1 This week: Bits, Bytes, and Integers Representing information as bits Bit-level manipulations Integers  Representation: unsigned and.
Bits and Bytes Boolean Algebra ( ) Boolean algebra Expressing in C.
University of Washington A few announcements Course web page – check often  cse.uw.edu/351  Schedule, policies, labs, homeworks, and everything else.
Bits and Bytes Topics Why bits? Representing information as bits
Carnegie Mellon 1 Bits, Bytes, and Integers : Introduction to Computer Systems 2 nd Lecture, Aug. 26, 2010 Instructors: Randy Bryant and Dave O’Hallaron.
Carnegie Mellon 1 Bits, Bytes, and Integers : Introduction to Computer Systems 2 nd and 3 rd Lectures, Aug 29 and Sep 3, 2013 Instructors: Randy.
Carnegie Mellon Bits, Bytes, and Integers (1-2) /18-243: Introduction to Computer Systems 2 nd Lecture, 19 May 2011 Instructors: Gregory Kesden.
Carnegie Mellon 1 Bits, Bytes, and Integers : Introduction to Computer Systems 2 nd and 3 rd Lectures, Aug 30 and Sep 4, 2012 Instructors: Dave O’Hallaron,
Lecture 2: Representing Numbers CS 2011 Fall 2014, Dr. Rozier.
Bits, Bytes, and Integers September 1, 2006 Topics Representing information as bits Bit-level manipulations Boolean algebra Expressing in C Representations.
CSCI-2500: Computer Organization Boolean Logic & Arithmetic for Computers (Chapter 3 and App. B)
1 University of Washington Today’s topics Just enough EE to be dangerous Memory and its bits, bytes, and integers Representing information as bits Bit-level.
Lecture 1 Introduction to Computer Architecture Topics Representations of Data Computer Architecture C Programming Unsigned Integers Signed magnitude Two’s.
Lecture 2 Two’s Complement Proofs Topics Two’s complement January 11, 2016 CSCE 212H Computer Architecture.
1 Manipulating Information (1). 2 Outline Bit-level operations Suggested reading –2.1.7~
Lecture 2 Ints revisited Topics Unsigned Integers Signed magnitude Two’s complement January 11, 2016 CSCE 212H Computer Architecture.
Number Systems and Representations Binary Representation Binary Representation Signed numbers Signed numbers Very small and very big numbers Very small.
1 Binghamton University Bits, Bytes, and Integers CS220: Introduction to Computer Systems 2 nd Lecture.
Instructors: Greg Kesden
Today’s Instructor: Randy Bryant
Memory, Data, & Addressing II CSE 351 Autumn 2017
Bits, Bytes, and Integers CSE 238/2038/2138: Systems Programming
Instructor: David Ferry
Representing Information
CSE351: Memory and data
Announcements VM on the website! Speedometer!
Bits and Bytes Topics Representing information as bits
Comp Org & Assembly Lang
Bits and Bytes Topics Representing information as bits
Bits and Bytes Boolean algebra Expressing in C
Bits and Bytes Topics Representing information as bits
Bits, Bytes, and Integers 2nd Lectures
Bits and Bytes Topics Representing information as bits
“The Class That Gives CMU Its Zip!”
Memory, Data, & Addressing II CSE 351 Summer 2018
Bits and Bytes Topics Representing information as bits
Comp Org & Assembly Lang
Comp Org & Assembly Lang
Bits, Bytes, and Integers Part 2 3rd Lectures
Comp Org & Assembly Lang
Bits, Bytes, and Integers
“The Class That Gives CMU Its Zip!”
“The Class That Gives CMU Its Zip!”
Lecture 2: Bits, Bytes, Ints
Presentation transcript:

Bits and Bytes Topics Why bits? Tell me Representing information as bits Binary/Hexadecimal Byte representations »numbers »characters and strings »Instructions Bit-level manipulations – READ BOOK Boolean algebra Expressing in C CS 105 bits.ppt CS 105 “Tour of the Black Holes of Computing!”

– 2 – CS 105 Binary Representations Base 2 Number Representation Represent as Represent as [0011]… 2 Represent X 10 4 as X 2 13 Electronic Implementation Easy to store with bistable elements - relays Reliably transmitted on noisy and inaccurate wires (media) Straightforward implementation of arithmetic functions 0.0V 0.5V 2.8V 3.3V 010

– 3 – CS 105 Byte-Oriented Mem Organization Programs Refer to Virtual Addresses Conceptually very large array of bytes Actually implemented with hierarchy of different memory types – SRAM, DRAM, Disk System provides address space private to particular “process” Program being executed Program can clobber its own data, but not that of others Compiler + Run-Time System Control Allocation Where different program objects should be stored Multiple mechanisms: static, stack, heap, etc. All allocation within single virtual address space 000FFF

– 4 – CS 105 Encoding Byte Values Byte = 8 bits Binary to Decimal: 0 10 to Hexadecimal to FF 16 Base 16 number representation Use characters ‘0’ to ‘9’ and ‘A’ to ‘F’ Write FA1D37B 16 in C as 0xFA1D37B »Or 0xfa1d37b Internet used term ‘Octet’ Why? A B C D E F Hex Decimal Binary

– 5 – CS 105 Word-Oriented Memory Organization Addresses Specify Byte Locations Address of first byte in word Addresses of successive words differ by 4 (32-bit) or 8 (64-bit) bit Words BytesAddr bit Words Addr = ?? Addr = ?? Addr = ?? Addr = ?? Addr = ?? Addr = ??

– 6 – CS 105 Data Representations Sizes of C Objects (in Bytes) C Data TypeTypical 32-bitIntel IA32 x86-64 char111 short222 int444 long448 long long888 float444 double888 long double810/1210/16 char *448 »Or any other pointer

– 7 – CS 105 Examining Data Representations Code to Print Byte Representation of Data Casting pointer to unsigned char * creates byte array typedef unsigned char *pointer; void show_bytes(pointer start, int len) { int i; for (i = 0; i < len; i++) printf("0x%p\t0x%.2x\n", start+i, start[i]); printf("\n"); } Printf directives: %p:Print pointer %x:Print Hexadecimal

– 8 – CS 105 show_bytes Execution Example int a = 15213; printf("int a = 15213;\n"); show_bytes((pointer) &a, sizeof(int)); Result (Linux): int a = 15213; 0x11ffffcb80x6d 0x11ffffcb90x3b 0x11ffffcba0x00 0x11ffffcbb0x00

– 9 – CS 105 Representing Integers int A = 15213; int B = ; long int C = 15213; Decimal:15213 Binary: Hex: 3 B 6 D 6D 3B 00 IA32, x86-64 A 3B 6D 00 Sun A 93 C4 FF IA32, x86-64 B C4 93 FF Sun B Two’s complement representation (Covered later) 00 6D 3B 00 x86-64 C 3B 6D 00 Sun C 6D 3B 00 IA32 C

– 10 – CS 105 Byte Ordering How should bytes within multi-byte word be ordered in memory? Religious Issue Conventions Suns, PowerPCs are “Big Endian” machines Least significant data byte has highest address Most significant data byte has lowest address Alphas, PCs are “Little Endian” machines Least significant byte has lowest address

– 11 – CS 105 Byte Ordering Example Big Endian Least significant byte has highest address Little Endian Least significant byte has lowest addressExample Variable x has 4-byte representation 0x Address given by &x is 0x100 0x1000x1010x1020x x1000x1010x1020x Big Endian Little Endian

– 12 – CS 105 Reading Byte-Reversed Listings Disassembly Text representation of binary machine code Generated by program that reads the machine code Example Fragment AddressInstruction CodeAssembly Rendition :5b pop %ebx :81 c3 ab add $0x12ab,%ebx c:83 bb cmpl $0x0,0x28(%ebx) Deciphering Numbers Value: 0x12ab Pad to 4 bytes: 0x000012ab Split into bytes: ab Reverse: ab

– 13 – CS 105 Representing Pointers int B = ; int *P = &B; // p is pointer, address values are different on different machines. FF 7F 00 0C 89 EC FF x86-64 P Different compilers & machines assign different locations to objects FB 2C EF FF Sun P FF BF D4 F8 IA32 P

– 14 – CS 105 Machine-Level Code Representation Encode Program as Sequence of Instructions Each simple operation Arithmetic operation Read or write memory Conditional branch Instructions encoded as bytes Alpha’s, Sun’s, Mac’s use 4 byte instructions »Reduced Instruction Set Computer (RISC) PC’s use variable length instructions »Complex Instruction Set Computer (CISC) Different instruction types and encodings for different machines Most code not binary compatible Programs are Byte Sequences Too - von Neumman!

– 15 – CS 105 Representing Instructions int sum(int x, int y) { return x+y; return x+y;} Different machines use totally different instructions and encodings Alpha sum FA 6B E C3 Sun sum For this example, Alpha & Sun use two 4-byte instructions Use differing numbers of instructions in other cases PC uses 7 instructions with lengths 1, 2, and 3 bytes Same for NT and for Linux NT / Linux not fully binary compatible E5 8B PC sum 45 0C EC 5D C3

– 16 – CS 105 Boolean Algebra – a review Developed by George Boole in 19th Century Algebraic representation of logic Encode “True” as 1 and “False” as 0And A&B = 1 when both A=1 and B=1 Not ~ A = 1 when A=0 Or A|B = 1 when either A=1 or B=1 Exclusive-Or (Xor) A^B = 1 when either A=1 or B=1, but not both

– 17 – CS 105 Bit-Level Operations in C follow Boolean Algebra Operations &, |, ~, ^ Available in C Apply to any “integral” data type long, int, short, char View arguments as bit vectors Arguments applied bit-wise Examples (Char data type) ~0x41 --> 0xBE ~ > ~0x00 --> 0xFF ~ > x69 & 0x55 --> 0x & > x69 | 0x55 --> 0x7D | >

– 18 – CS 105 Contrast: Logic Operations in C Contrast to Logical Operators &&, ||, ! View 0 as “False” Anything nonzero as “True” -- key point Always return 0 or 1 Early termination Examples (char data type) !0x41 --> 0x00 !0x00 --> 0x01 !!0x41 --> 0x01 0x69 && 0x55 --> 0x01 0x69 || 0x55 --> 0x01 p && *p ( avoids null pointer access) ??

– 19 – CS 105 Shift Operations Left Shift: x << y Shift bit-vector x left y positions Throw away extra bits on left Fill with 0’s on right Right Shift: x >> y Shift bit-vector x right y positions Throw away extra bits on right Logical shift Fill with 0’s on left Arithmetic shift Replicate most significant bit Useful with two’s complement integer representation Argument x << Log. >> Arith. >> Argument x << Log. >> Arith. >>

– 20 – CS 105 Cool Stuff with Xor void funny(int *x, int *y) { *x = *x ^ *y; /* #1 */ *x = *x ^ *y; /* #1 */ *y = *x ^ *y; /* #2 */ *y = *x ^ *y; /* #2 */ *x = *x ^ *y; /* #3 */ *x = *x ^ *y; /* #3 */} // x, y not equal Bitwise XOR is form of addition With extra property that every value is its own additive inverse A ^ A = 0 BA Begin BA^B 1 (A^B)^B = AA^B 2 A(A^B)^A = B 3 AB End *y*x

– 21 – CS 105 Main Points It’s All About Bits & Bytes Numbers Programs Text Different Machines Follow Different Conventions Word size Byte ordering Representations Boolean Algebra is Mathematical Basis Basic form encodes “false” as 0, “true” as 1 General form like bit-level operations in C Good for representing & manipulating sets

– 22 – CS 105 Practice Problems