binary numbers
play

Binary Numbers 723 Binary Numbers 723 = 7x100 + 2x10 + 3x1 Binary - PowerPoint PPT Presentation

Oct 02, 2022 •470 likes •1.23k views

Binary Numbers 723 Binary Numbers 723 = 7x100 + 2x10 + 3x1 Binary Numbers 723 = 7x100 + 2x10 + 3x1 = 7x10 2 + 2x10 1 + 3x10 0 Binary Numbers 5349 = 5x10 3 + 3x10 2 + 4x10 1 + 9x10 0 Binary Numbers Why base 10? Binary Numbers 257 (base 8)

  1. Binary Numbers 723

  2. Binary Numbers 723 = 7x100 + 2x10 + 3x1

  3. Binary Numbers 723 = 7x100 + 2x10 + 3x1 = 7x10 2 + 2x10 1 + 3x10 0

  4. Binary Numbers 5349 = 5x10 3 + 3x10 2 + 4x10 1 + 9x10 0

  5. Binary Numbers Why base 10?

  6. Binary Numbers 257 (base 8) 2x8 2 + 5x8 1 + 7x8 0 2x64 + 5x8 + 7x1 175 (base 10)

  7. Binary Numbers 0110 (base 2) 0x2 3 + 1x2 2 + 1x2 1 + 0x2 0 0x8 + 1x4 + 1x2 + 0x1 6 (base 10)

  8. Binary Numbers 2 1 2 0 00 0 01 1 10 2 max value = 2 2 -1 11 3 2-bit binary number

  9. Binary Numbers 000 0 001 1 010 2 011 3 100 4 101 5 110 6 111 7 max value = 2 3 -1 3-bit binary number

  10. Binary Numbers 0000 0 0001 1 0010 2 0011 3 0100 4 0101 5 0110 6 0111 7 1000 8 1001 9 1010 10 1011 11 1100 12 1101 13 1110 14 max value = 2 4 -1 1111 15 4-bit binary number

  11. Binary Numbers (why?) reliability!

  12. Binary Numbers (why?) 9 9 9 9 8 8 8 8 7 7 7 7 6 6 6 6 5 5 5 5 4 4 4 4 3 3 3 3 2 2 2 2 1 1 1 1 0 0 0 0 0 4 6 7

  13. Binary Numbers (why?) 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 0 0 1

  14. Binary Numbers How do we encode negative numbers?

  15. Binary Numbers use left-most bit to represent sign 0 = “+” 1 = “-”

  16. Binary Numbers sign 2 1 2 0 000 0 001 1 010 2 011 3 100 101 110 111 3-bit signed binary number

  17. Binary Numbers sign 2 1 2 0 000 0 001 1 010 2 011 3 100 -0 ??? 101 -1 110 -2 111 -3 3-bit signed binary number

  18. Binary Numbers (two’s complement) 1. start with an unsigned 4-bit binary number where left- most bit is 0 • 0110 = 6

  19. Binary Numbers (two’s complement) 1. start with an unsigned 4-bit binary number where left- most bit is 0 • 0110 = 6 2. complement your binary number (flip bits) • 1001

  20. Binary Numbers (two’s complement) 1. start with an unsigned 4-bit binary number where left- most bit is 0 • 0110 = 6 2. complement your binary number (flip bits) • 1001 3. add one to your binary number • 1010 = -6

  21. Binary Numbers (two’s complement) positive complement +1 negative 0 000 0 1 001 -1 2 010 -2 3 011 -3 3-bit signed binary number

  22. Binary Numbers (two’s complement) positive complement +1 negative 0 000 0 1 001 110 111 -1 2 010 -2 3 011 -3 3-bit signed binary number

  23. Binary Numbers (two’s complement) positive complement +1 negative 0 000 0 1 001 110 111 -1 2 010 101 110 -2 3 011 -3 3-bit signed binary number

  24. Binary Numbers (two’s complement) positive complement +1 negative 0 000 0 1 001 110 111 -1 2 010 101 110 -2 3 011 100 101 -3 3-bit signed binary number

  25. Binary Numbers (two’s complement) positive complement +1 negative 0 000 111 0 1 001 110 111 -1 2 010 101 110 -2 3 011 100 101 -3 3-bit signed binary number

  26. Binary Numbers (two’s complement) positive complement +1 negative !!! 0 000 111 000 0 1 001 110 111 -1 2 010 101 110 -2 3 011 100 101 -3 3-bit signed binary number

  27. Binary Numbers (two’s complement) positive complement +1 negative 0 000 111 000 0 1 001 110 111 -1 2 010 101 110 -2 3 011 100 101 -3 we lost a number?

  28. Binary Numbers (two’s complement) positive complement +1 negative 0 000 111 000 0 1 001 110 111 -1 2 010 101 110 -2 3 011 100 101 -3 100 we lost a number?

  29. Binary Numbers (two’s complement) complement -1 100

  30. Binary Numbers (two’s complement) 010 -2 complement -1 011 -1 011 100 100 101 +1 110 +2

  31. Binary Numbers (two’s complement) complement -1 100 011 100

  32. Binary Numbers (two’s complement) complement -1 4 100 011 100

  33. Binary Numbers (two’s complement) positive complement +1 negative 0 000 111 000 0 1 001 110 111 -1 2 010 101 110 -2 3 011 100 101 -3 100 -4 n-bit unsigned binary numbers: 0...2 n -1

  34. Binary Numbers (two’s complement) positive complement +1 negative 0 000 111 000 0 1 001 110 111 -1 2 010 101 110 -2 3 011 100 101 -3 100 -4 n-bit signed binary numbers: -2 n-1 ... 2 n-1 -1

  35. Binary Numbers (two’s complement) 0010 2 0010 2 + ---- + - 0100 4 summing unsigned binary numbers is easy

  36. Binary Numbers (two’s complement) 0010 2 1010 -2 + ---- + - 1100 0 ? summing signed binary numbers

  37. Binary Numbers (two’s complement) 0011 3 1011 -3 + ---- + - 1110 0 ? summing signed binary numbers

  38. Binary Numbers (two’s complement) 0010 -> 1101 -> 1110 0010 2 -2 + ---- + - 0 summing signed (2‘s complement) binary numbers

  39. Binary Numbers (two’s complement) 0010 -> 1101 -> 1110 0010 2 1110 -2 + ---- + - 0000 0 summing signed (2‘s complement) binary numbers

  40. Binary Numbers (two’s complement) 0011 -> 1100 -> 1101 0011 3 -3 + ---- + - 0 summing signed (2‘s complement) binary numbers

  41. Binary Numbers (two’s complement) 0011 -> 1100 -> 1101 0011 3 1101 -3 + ---- + - 0000 0 summing signed (2‘s complement) binary numbers

  42. Binary Numbers (decoding two’s complement) 0111 = ? 4-bit signed (two’s complement) binary number

  43. Binary Numbers (decoding two’s complement) 0111 = 7 4-bit signed (two’s complement) binary number

  44. Binary Numbers (decoding two’s complement) 1011 = ? 4-bit signed (two’s complement) binary number

  45. Binary Numbers (decoding two’s complement) subtract 1 1011 1010 4-bit signed (two’s complement) binary number

  46. Binary Numbers (decoding two’s complement) subtract 1 complement 1011 1010 0101 4-bit signed (two’s complement) binary number

  47. Binary Numbers (decoding two’s complement) subtract 1 complement 1011 1010 0101 5 4-bit signed (two’s complement) binary number

  48. Binary Numbers (decoding two’s complement) 1011 = -5 4-bit signed (two’s complement) binary number

  49. Binary Numbers How do we encode fractional numbers?

  50. Binary Numbers ± mantissa x base ± exponent

  51. Boolean Logic (variables) 1 = True 0 = False

  52. Boolean Logic (truth tables) a b a and b 1 1 1 1 0 0 0 1 0 0 0 0 a and b

  53. Boolean Logic (truth tables) a b a or b 1 1 1 1 0 1 0 1 1 0 0 0 a or b

  54. Boolean Logic (truth tables) a not a 1 0 0 1 not a

  55. Boolean Logic (truth tables) input output (boolean variable) (boolean variable) a , b a and b a or b not a

  56. Gates a b a and b 1 1 1 1 0 0 0 1 0 0 0 0 a a and b ⋅ b

  57. Gates a b a or b 1 1 1 1 0 1 0 1 1 0 0 0 a a or b + b

  58. Gates a not a 1 0 0 1 a not a

  59. Building Gates (transistors) power power input input 0 1

  60. Building Gates (transistors) power 0 0

  61. Building Gates (transistors) power 0 0 0

  62. Building Gates (transistors) power 0 1

  63. Building Gates (transistors) power 0 1 0

  64. Building Gates (transistors) power 1 0

  65. Building Gates (transistors) power 1 0 0

  66. Building Gates (transistors) power 1 1

  67. Building Gates (transistors) power 1 1 1

  68. Building Gates (transistors) power power power power 1 0 1 0 1 1 0 0 0 1 0 0

  69. Building Gates (transistors) power power power power 1 0 1 0 1 1 0 0 0 1 0 0 AND gate

  70. Building Gates (transistors) 0 1 OR gate

  71. Building Gates (transistors) power 0 1 1 OR gate

  72. Building Gates (transistors) power 1 1 1 OR gate

  73. Building Gates (transistors) power 0 0 0 OR gate

  74. Building Gates (transistors) power 1 resistor 0 junk NOT gate

  75. Building Gates (transistors) power 0 resistor 1 junk NOT gate

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Binary Numbers Binary numbers look like this Binary Numbers or Binary Code Binary numbers or

Binary Numbers Binary numbers look like this Binary Numbers or Binary Code Binary numbers or

Binary Numbers Binary numbers look like this Binary Numbers or Binary Code Binary numbers or binary code are used by computers and digital devices to talk to each other. It is used to give commands to the computer or a way to enter data

165 views • 12 slides
Negative Numbers and Binary operations Eric McCreath Binary Addition Adding binary numbers is

Negative Numbers and Binary operations Eric McCreath Binary Addition Adding binary numbers is

Negative Numbers and Binary operations Eric McCreath Binary Addition Adding binary numbers is very similar to how you would add large decimal numbers in primary school It involves positioning the numbers such that the columns line up in their

562 views • 10 slides
1.3 - Binary Point Numbers and the ASCII Table! What are they? Binary point numbers are the way

1.3 - Binary Point Numbers and the ASCII Table! What are they? Binary point numbers are the way

1.3 - Binary Point Numbers and the ASCII Table! What are they? Binary point numbers are the way numbers like 42.625 are represented in binary. But first, well start the other way Take a number like: 1101.101 2 And remember our columns?

96 views • 5 slides
Fixed and Floating-point Numbers Eric McCreath Fractional binary numbers Remember how the

Fixed and Floating-point Numbers Eric McCreath Fractional binary numbers Remember how the

Fixed and Floating-point Numbers Eric McCreath Fractional binary numbers Remember how the meaning of the digits in a binary number is defined: Note the binary radix point For example, the binary number: means 2 Binary Converting a

449 views • 7 slides
Binary Numbers Calculate your age Binary & decimal differences In binary 1 represents

Binary Numbers Calculate your age Binary & decimal differences In binary 1 represents

Binary Numbers Calculate your age Binary & decimal differences In binary 1 represents on Fun Facts Why 10 digits? Because and the 0 represents off people typically have 10 fingers and 10 toes, making it easy for counting! 2

119 views • 10 slides
Fixed and Floating Point Numbers Eric McCreath Fractional binary numbers Remember how the

Fixed and Floating Point Numbers Eric McCreath Fractional binary numbers Remember how the

Fixed and Floating Point Numbers Eric McCreath Fractional binary numbers Remember how the meaning of the digits in a binary number is defined: note how there is a binary radix point. So for example the binary number: means 2 Binary

549 views • 7 slides
Binary Numbers X. Zhang Fordham Univ. 1 Numeral System A way for expressing numbers, using

Binary Numbers X. Zhang Fordham Univ. 1 Numeral System A way for expressing numbers, using

Binary Numbers X. Zhang Fordham Univ. 1 Numeral System A way for expressing numbers, using symbols in a consistent manner. " 11 " can be interpreted differently: in the binary symbol: three in the decimal

735 views • 20 slides
. 1 b i b i 1 b 2 b 1 b 0 b 1 b 2 b 3 b j 1/2 1/4

. 1 b i b i 1 b 2 b 1 b 0 b 1 b 2 b 3 b j 1/2 1/4

12/9/15 Fractional Binary Numbers 2 i 2 i 1 Floating-point numbers 4 2 . 1 b i b i 1 b 2 b 1 b 0 b 1 b 2 b 3 b j 1/2 1/4 Fractional binary numbers 1/8 IEEE

602 views • 3 slides
CS101 Lecture 11: Data Representation: Binary Numbers Number Systems Binary Numbers Aaron

CS101 Lecture 11: Data Representation: Binary Numbers Number Systems Binary Numbers Aaron

1/23/13 CS101 Lecture 11: Data Representation: Binary Numbers Number Systems Binary Numbers Aaron Stevens (azs@bu.edu) 23 January 2013 Computer Science Computer Science 1 1/23/13 Computer Science Computer Science !!! MATH WARNING !!! TODAY

486 views • 15 slides
Binary There are 10 types of people in the world those that understand binary and those

Binary There are 10 types of people in the world those that understand binary and those

Binary There are 10 types of people in the world those that understand binary and those that dont. What is binary? You and I write numbers like this: twelve is 12, sixty eight is 68, and one hundred is 100 Binary is a number

525 views • 26 slides
LECTURE 2 Review 1 Binary Math and Assembly BINARY MATH In this section, we review Binary

LECTURE 2 Review 1 Binary Math and Assembly BINARY MATH In this section, we review Binary

LECTURE 2 Review 1 Binary Math and Assembly BINARY MATH In this section, we review Binary to decimal conversions and vice versa IEEE 754 Floating point representations Binary Arithmetic Decimal representation of binary numbers

1.66k views • 118 slides
Bitwise Operators Number Representation Recap Humans think about numbers in decimal Computers

Bitwise Operators Number Representation Recap Humans think about numbers in decimal Computers

Bitwise Operators Number Representation Recap Humans think about numbers in decimal Computers think about numbers in binary Base conversion to go between Hex is more human-readable than binary All information on a computer is in binary

250 views • 7 slides
Digital Design Discussion: Numbers Binary to Decimal Conversion Decimal to Binary Conversion

Digital Design Discussion: Numbers Binary to Decimal Conversion Decimal to Binary Conversion

Principles Of Digital Design Discussion: Numbers Binary to Decimal Conversion Decimal to Binary Conversion Floating-Point Conversion Positional Number System Each number is represented by a string of digits, in which the position of each

533 views • 6 slides
Binary Numbers 2 Homework #1 Assigned today!

Binary Numbers 2 Homework #1 Assigned today!

Computer Systems and Networks ECPE 170 Jeff Shafer University of the Pacific Binary Numbers 2 Homework #1 Assigned today!

644 views • 39 slides
Binary Numbers 2 Recap - von Neumann Model How

Binary Numbers 2 Recap - von Neumann Model How

Computer Systems and Networks ECPE 170 Jeff Shafer University of the Pacific Binary Numbers 2 Recap - von Neumann Model How

797 views • 58 slides
BY THE NUMBERS BY THE NUMBERS BY THE NUMBERS BY THE NUMBERS BY THE NUMBERS BY THE NUMBERS

BY THE NUMBERS BY THE NUMBERS BY THE NUMBERS BY THE NUMBERS BY THE NUMBERS BY THE NUMBERS

BY THE NUMBERS BY THE NUMBERS BY THE NUMBERS BY THE NUMBERS BY THE NUMBERS BY THE NUMBERS Pre-roll, Outstream, Video Production, OTT, Social Video Display, Audience Extension, Mobile Precise, Programmatic, Retargeting, Social, Native SEM,

476 views • 31 slides
Week 8 Oliver Kullmann Binary trees The notion BinaryTrees of binary search tree Tree

Week 8 Oliver Kullmann Binary trees The notion BinaryTrees of binary search tree Tree

CS 270 Algorithms Week 8 Oliver Kullmann Binary trees The notion BinaryTrees of binary search tree Tree traversal Binary trees 1 Queries in binary The notion of binary search tree search trees 2 Insertion Tree

1.02k views • 49 slides
Linked Structures Songs, Games, Movies Part III Fall 2013 Carola Wenk Biological Structures

Linked Structures Songs, Games, Movies Part III Fall 2013 Carola Wenk Biological Structures

Linked Structures Songs, Games, Movies Part III Fall 2013 Carola Wenk Biological Structures Nature has evolved vascular and nervous systems in a hierarchical manner so that nutrients and signals can quickly reach their Human Nervous System

707 views • 33 slides
A Quick Review Decimal to binary Binary to decimal Binary to hexadecimal

A Quick Review Decimal to binary Binary to decimal Binary to hexadecimal

A Quick Review Decimal to binary Binary to decimal Binary to hexadecimal Hexadecimal to binary Hexadecimal to Decimal Binary addition Binary subtraction Binary shift Decimal to Binary 146d = ????????b 146/2

91 views • 7 slides
expression trees Oct. 27, 2017 1 Binary tree: each node has at most two children. 2 Maximum

expression trees Oct. 27, 2017 1 Binary tree: each node has at most two children. 2 Maximum

COMP 250 Lecture 21 binary trees, expression trees Oct. 27, 2017 1 Binary tree: each node has at most two children. 2 Maximum number of nodes in a binary tree? Height (e.g. 3) 3 Maximum number of nodes in a binary tree? Height

637 views • 53 slides
Binary Methods Programming: Non-issues the C LOS Perspective Types, Classes, Inheritance Method

Binary Methods Programming: Non-issues the C LOS Perspective Types, Classes, Inheritance Method

C LOS Binary Methods Didier Verna Introduction Binary Methods Programming: Non-issues the C LOS Perspective Types, Classes, Inheritance Method comb. Usage Introspection Binary function class Didier Verna Implementation

763 views • 26 slides
Algorithms 1. Existence 2. Efficiency Time Space Worst case behavior analysis as a

Algorithms 1. Existence 2. Efficiency Time Space Worst case behavior analysis as a

Algorithms 1. Existence 2. Efficiency Time Space Worst case behavior analysis as a function of input size Asymptotic growth: O W Q o w Donald Knuth Upper Bounds Definition: f(n) = O(g(n)) $ c,k > 0 ' 0 f(n) c

901 views • 31 slides
Symmetry Breaking Polytopes: A Framework for Symmetry Handling in Binary Programs Christopher

Symmetry Breaking Polytopes: A Framework for Symmetry Handling in Binary Programs Christopher

Symmetry Breaking Polytopes: A Framework for Symmetry Handling in Binary Programs Christopher Hojny joint work with Marc E. Pfetsch Technische Universitt Darmstadt Department of Mathematics Aussois Combinatorial Optimization Workshop 2018

795 views • 46 slides
Twisted 4 -normal form for elliptic curves David Kohel Institut de Math ematiques de

Twisted 4 -normal form for elliptic curves David Kohel Institut de Math ematiques de

Introduction State of the Art Curve Origins Efficient arithmetic Comparisons and conclusion Twisted 4 -normal form for elliptic curves David Kohel Institut de Math ematiques de Marseille Eurocrypt 2017, Paris, 1 May 2017 Introduction

552 views • 16 slides

More recommend