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CS 231 Intro & Base Conversions

CS 231 Intro & Base Conversions. Celal Ziftci Aug 26, 2005. Announcements. Mallard is up. Try to log on and take the first quiz (due Monday, Aug 29) Course webpage is down Mallard link is posted on the newsgroup (https://mallard2.cites.uiuc.edu/CS231/)

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CS 231 Intro & Base Conversions

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  1. CS 231Intro & Base Conversions Celal Ziftci Aug 26, 2005

  2. Announcements • Mallard is up. Try to log on and take the first quiz (due Monday, Aug 29) • Course webpage is down • Mallard link is posted on the newsgroup(https://mallard2.cites.uiuc.edu/CS231/) • First homework assignment to be released sometime next week

  3. Tips for CS 231 • Don’t hesitate to: • Ask questions • Interrupt when you don’t understand • Be comfortable with binary and hex • Learn device inputs & outputs • Allows abstraction • Easier to understand • Show your work

  4. Tips for CS 231 • Efficiency is important! • Neatness is important! • Unreadable solutions are considered wrong • Readable ones are neat, short (big favor for both you and the graders)

  5. Digits vs. bits • Digits = powers of 10 … 100, 10, 1, 1/10, 1/100, 1/1000 … … 102, 101, 100, 10-1, 10-2, 10-3 … Ex: (36.25)10 = 3*10 + 6*1 + 2*1/10 + 5* 1/100 • Bits = powers of 2 … 8, 4, 2, 1, 1/2, 1/4, 1/8 … … 23, 22, 21, 20, 2-1, 2-2, 2-3 … Ex: (100100.01)2 = 1*32 + 1*4 + 1*1/4

  6. Binary to decimal • add powers that have a 1 (101001)2 = 32 + 8 + 1 (0.1001)2 = 1/2 + 1/16 (10110.1011)2 = ? 16 + 4 + 2 + 1/2 + 1/8 + 1/16 = 22.6875

  7. Decimal to binary • Left of decimal point • Repeatedly divide integer part by 2 until you get 0 • Read remainders bottom to up 22 = (?)2 22 11 R 0 5 R 1 2 R 1 1 R 0 0 R 1

  8. Decimal to binary • Left of decimal point • Repeatedly divide integer part by 2 until you get 0 • Read remainders bottom to up 22 = (10110)2 22 11 R 0 5 R 1 2 R 1 1 R 0 0 R 1

  9. Decimal to binary • Right of decimal point • Repeatedly multiply fractional part by 2 until you get 1 • Read integer portion top to bottom 0.8125 = (?)2 0.8125 1.6250 1.25 0.5 1.0

  10. Decimal to binary • Right of decimal point • Repeatedly multiply fractional part by 2 until you get 1 • Read integer portion top to bottom 0.8125 = (0.1101)2 0.8125 1.6250 1.25 0.5 1.0

  11. Decimal to binary • What if there are both left and right of the decimal point? • Do them separately and combine 22.8125 = (?)2

  12. Decimal to binary • What if there are both left and right of the decimal point? • Do them separately and combine 22.8125 = (?)2 22 11 R 0 5 R 1 2 R 1 1 R 0 0 R 1 0.8125 1.6250 1.25 0.5 1.0

  13. Decimal to binary • What if there are both left and right of the decimal point? • Do them separately and combine 22.8125 = (10110.1101)2 22 11 R 0 5 R 1 2 R 1 1 R 0 0 R 1 0.8125 1.6250 1.25 0.5 1.0 up down

  14. Decimal to binary • Toy example3.25 = (?)2 0. 25 0.50 1.0 3 1 R 1 0 R 1

  15. Decimal to binary • Toy example3.25 = (11.01)2 0. 25 0.50 1.0 3 1 R 1 0 R 1

  16. Hexadecimal base • Hex digits = powers of 16 … 256, 16, 1, 1/16, 1/256 … … 162, 161, 160, 16-1, 16-2 … • use digits 0-9, A-F • A=10, B=11, C=12, D=13, E=14, F=15 • often preceded by 0x • book subscript notation (24.4)16 Ex: (24.4)16 = 2*16 + 4*1 + 4*1/16

  17. Hexadecimal base dec. hex binary 0 0 0000 1 1 0001 2 2 0010 3 3 0011 4 4 0100 5 5 0101 6 6 0110 7 7 0111 8 8 1000 9 9 1001 10 A 1010 11 B 1011 12 C 1100 13 D 1101 14 E 1110 15 F 1111 • Hex (hexadecimal) • Hex digit is a group of 4 bits • Memorize this table!!

  18. Binary to Hex • Hex (hexadecimal) • Group from decimal point outward • Pad with zeros to get groups of 4 (1101101001010.101001)2 (0001 1011 0100 1010 . 1010 0100)2 1 B 4 A . A 4 (1101101001010.101001)2 = (1B4A.A4)16

  19. Octal base • Octal digits = powers of 8 … 64, 8, 1, 1/8, 1/64 … … 82, 81, 80, 8-1, 8-2 … • use digits 0-7 • sometimes preceded by 0 • book subscript notation (24.4)8 Ex: (44.2)8 = 4*8 + 4*1 + 2*1/8

  20. Octal base dec. octal binary 0 0 000 1 1 001 2 2 010 3 3 011 4 4 100 5 5 101 6 6 110 7 7 111 • Octal • Octal digits are groups of 3 bits • Pad with zeros

  21. Binary to Octal • Octal • Group from decimal point outward • Pad with zeros to get groups of 3 (1101101001010.101001)2 (001 101 101 001 010 . 101 001)2 1 5 5 1 2 . 5 1 (1101101001010.101001)2 = (15512.51) 8

  22. Other conversions • What about other conversions such as: • Octal  Hex • Decimal  Hex • … • Use other conversions you already know • Octal  Binary  Hex • Decimal  Binary  Hex

  23. Summary • Decimal  BinaryBinary  Decimal • Binary  HexBinary  Octal • Other conversions • Use the conversions you already know

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