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CS 231 – Spring 2006 Intro & Base Conversions

CS 231 – Spring 2006 Intro & Base Conversions. Celal Ziftci Jan 27, 2005. Announcements. Due dates of the quizzes Quiz 0 and Quiz 1 extended to Monday, January 30. First homework assignment to be released Monday, January 30 Office hours start next week.

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CS 231 – Spring 2006 Intro & Base Conversions

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  1. CS 231 – Spring 2006Intro & Base Conversions Celal Ziftci Jan 27, 2005

  2. Announcements • Due dates of the quizzes Quiz 0 and Quiz 1 extended to Monday, January 30. • First homework assignment to be released Monday, January 30 • Office hours start next week. • Follow the newsgroup and course webpage. • Important announcements and discussion.

  3. Tips for CS 231 • 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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