The sad, strange tale of the boy with only two fingers - OR - An introduction to binary for non-robot human people

Most people know that computers are "just a bunch of ones and zeroes," but few understand what that really means. How do ones and zeros become numbers, words, and pictures? This talk starts at the beginning, explaining binary numbers and shows how they are used to describe basic datatypes. We begin to uncover what the statement "just a bunch of ones and zeroes" really means.

Transcript

1. The sad, strange tale of the boy with only two fingers: an introduction to binary for non-robot, human people
2. A bunch of ones and zeroes
3. This?
4. All hardware is analog.
5. Analog is prone to noise.
6. Binary simplifies low and high voltage into ON or OFF.
7. It can be encoded into almost any medium.
8. “Digital” Media Punchcard CD-ROM CD-Rom This crap Redstone
9. Understanding Binary.
10. 1010101000111110110110010010011101010 0111010000110101010110010010100001011 1101001110100110101010101011100100101 1010010101001010101001000110000011110 1011010101001010010101000101001010010 1000111010111100110010010011101010011 1010000110101010110010010100001100001 1011110100111010011010101010101110010 0101101001010100101010100100011000001 1110101101010100101001010100010100101 Binary is scary.
11. Let’s start with something less scary, decimal numbers. 0123456789
12. • …8…9…10 • …98…99…100 • …999,998… 999,999… 1,000,000 Run out of symbols -> start a new column.
13. The number 10 is totally arbitrary.
14. 1 2 3 4 5 6 7 8 9 10 Digits.
15. youtu.be/U6xJfP7-HCc 2 3 4 5 6 7 8 9 X 3 1 10
16. Binary:
 Same ideas;
 different number of digits.
17. 1 10
18. • 0…1…10 • 10…11…100 • 1111100…1111101…1111110… 1111111… 1000000 Run out of symbols -> start a new column.
19. 1 1 1 1 1 1 1 1
 Byte (8 bits) Nibble (4 bits) 1 Bit Bits & Bytes
20. 128 64 32 16 8 4 2 1 1 1 1 1 1 1 1 1 128+64+32+16+8+4+2+1=255 Value of each Bit in a Byte Powers of 2
21. Bytes are often represented as Hexadecimal numbers. Each byte gets 2 hex-digits. 00...FF
22. 2 3 4 5 6 7 8 9 A B 1 C D E F 10
23. Why?
24. FFFFFF Is much easier than 111111111111111111111111 Or 16,777,216
25. 1 0 0 1
 
 
 0 0 1 1
 
 
 1 1 0 1
 Test your might!
26. 1 0 0 1
 
 
 0 0 1 1
 
 
 1 1 0 1
 Test your might! = 9 = 3 = 13 
 8 4 2 1
 
 8 4 2 1
 
 8 4 2 1
27. 1001 (9)
 + 1100 (12)
 ----------
 10101 (21) Arithmetic works the same way.
28. 1001 (9)
 x 1100 (12)
 ——————————- 
 0000 xxx 
 00000 x xxx
 100100 x xxx
 + 1001000 x xxx 
 -—————————————-
 1101100 (108) Arithmetic works the same way.
29. Memory.
30. Memory. TuringMachine.
31. Memory. TuringMachine. “Turing's greatest contribution to the development of the digital computer [was the] idea of controlling the function of a computing machine by storing a program of … numerically, encoded instructions in the machine's memory” http://www.alanturing.net/
32. Data Types. Representing
33. Booleans.
34. Booleans
 1 bit of data
 0 = false
 1 = true
35. Numbers.
36. Whole numbers.
37. Integers are represented by sets of 1s and 0s 7 = 0111
38. How many 1’s and 0’s determine the maximum size of the number 8 bits (0 to 255) 16 bits (0 to 64,000ish) 32 bits (0 to 4.3 billionish)
39. Use 1 bit to allow negatives. This cuts the maximum number in half. 8 bits (-127 to 127) 16 bits (-32K to 32K) 32 bits (-2.2B to 2.2B)
40. Decimal numbers.
41. • Very large or very small numbers. • Sacrifice accuracy for range. Floating point
42. The way it works is complicated!
 

43. A vastly simplified version… that is still pretty confusing 1 + 1/2 + 1/4 + 1/8 + 1/16… 1 0 1 1… 24 bits determine the base number 7 bits for the exponent 1.2345678 1 bit for the sign 1 0001101 × ×29 - -632.0987136
44. 0.2 + 0.1 == 0.3; 0.30000000000000004 0.2 + 0.1; // Javascript // 8-((((((((( 0.2 + 0.1 == 0.3; // FALSE!
45. Arrays.
46. Can be as simple as 3 numbers… • A place to look in memory • The number of bits in each item • The number of items An array is a set of multiple values.
47. 0 0 1 0 0 1 0 1 0 0 1 0 Data in memory location 0 location 4 location 8 Array of pointers
48. Text.
49. Characters.
50. Characters are individual letters, numbers, or other glyphs.
 
 Each number maps to a glyph.
51. ASCII.
52. • A basic type of encoding. • 255 characters. • 1 byte each. ASCII.
53. The letter ‘A’ maps to 65 in ASCII
 
 0100 0001
54. Unicode.
55. • 1 million + glyphs • Allows a huge number of characters to be represented with as few bits as possible. • Uses a form of data compression. Unicode.
56. Some bits in each byte indicate whether there is another byte after it.
57. Strings.
58. • An array of characters. • A null character (eight 0s) marks the end of a string. Strings.
59. 0100 1101 “M” 0110 1001 “i” 0110 1101 “m” 0111 0011 “s” 0000 0000 “ ”
 
 “Mims ”
60. Digital music.
61. Approximate of amplitude (volume) Time Encoding a waveform into binary Each sample is a 16-bit integer
62. Images.
63. Hex colors. Remember hexadecimal from a few slides ago?
64. Test your might! FF0000
65. Test your might! FF0000 FF0000
66. 00FF00
67. 00FF00 00FF00
68. 0000FF
69. 0000FF 0000FF
70. FFFFFF
71. FFFFFF FFFFFF
72. 6F43B2
73. 6F43B2 6F43B2
74. 6F43B2 6F43B2 A bit redish Not very green Sort of a lot of blue 6F43B2
75. Colors are 24 bits (aka 3 bytes or 6 hex digits) Colors sometimes have an alpha channel (32 bits) Each color channel has 256 possible brightness levels
76. In their simplest form, images are arrays of colors (plus some metadata)
78. Everything else.
79. Typed Arrays ArrayBuffer DataView Bitwise operators |,&,^,~,>>,<< // Javascript http://developer.mozilla.org/en/docs/Web/JavaScript/Typed_arrays
80. A bunch of ones and zeroes
81. Mims H. Wright Freelance Software Developer mims@mimswright.com @mimshwright github.com/mimshwright/