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CS 241: Systems Programming Lecture 12. Bits and Bytes 1 Fall 2019 Prof. Stephen Checkoway 1 Computers use binary Everything in a computer is stored and manipulated as a collection of bits The bits mean something only in how they are

  1. CS 241: Systems Programming Lecture 12. Bits and Bytes 1 Fall 2019 Prof. Stephen Checkoway � 1

  2. Computers use binary Everything in a computer is stored and manipulated as a collection of bits ‣ The bits mean something only in how they are used, not what they are Example with 32-bits: 01000011010100110100001101001001 ‣ As a integer: 1129530185 ‣ As a (single-precision) floating point number: 211.262833 ‣ As a sequence of four ASCII characters: CSCI ‣ As 32-bit x86 instructions: 
 inc ebx 
 push ebx 
 inc ebx 
 dec ecx � 2

  3. Base 10 review � 3

  4. Base 10 review Given a decimal (base 10) number 1253 10 � 3

  5. Base 10 review Given a decimal (base 10) number 1253 10 ‣ 3 ones (10 0 ) � 3

  6. Base 10 review Given a decimal (base 10) number 1253 10 ‣ 3 ones (10 0 ) ‣ 5 tens (10 1 ) � 3

  7. Base 10 review Given a decimal (base 10) number 1253 10 ‣ 3 ones (10 0 ) ‣ 5 tens (10 1 ) ‣ 2 hundreds (10 2 ) � 3

  8. Base 10 review Given a decimal (base 10) number 1253 10 ‣ 3 ones (10 0 ) ‣ 5 tens (10 1 ) ‣ 2 hundreds (10 2 ) ‣ 1 thousand (10 3 ) 10 3 10 2 10 1 10 0 
 1 2 5 3 � 3

  9. Base 8 (Octal) � 4

  10. Base 8 (Octal) Only uses the digits 0-7 ‣ In C, literal starts with leading 0 � 4

  11. Base 8 (Octal) Only uses the digits 0-7 ‣ In C, literal starts with leading 0 Given a octal (base 8) number 02345 ‣ 5 ones (8 0 ) ‣ 4 eights (8 1 ) ‣ 3 sixty-fours (8 2 ) ‣ 2 five hundred twelves (8 3 ) � 4

  12. Base 8 (Octal) Only uses the digits 0-7 ‣ In C, literal starts with leading 0 Given a octal (base 8) number 02345 ‣ 5 ones (8 0 ) ‣ 4 eights (8 1 ) ‣ 3 sixty-fours (8 2 ) ‣ 2 five hundred twelves (8 3 ) 8 3 8 2 8 1 8 0 
 2 3 4 5 � 4

  13. Base 16 (Hexadecimal) � 5

  14. Base 16 (Hexadecimal) Single place has values of 0-15 ‣ Need digits larger than 9. Use A=10, B=11, …, F=15 ‣ In C, starts with a leading 0x or 0X � 5

  15. Base 16 (Hexadecimal) Single place has values of 0-15 ‣ Need digits larger than 9. Use A=10, B=11, …, F=15 ‣ In C, starts with a leading 0x or 0X Given a hexadecimal (base 16) number 0x04E5 ‣ 5 ones (16 0 ) ‣ 14 sixteens (16 1 ) ‣ 4 two hundred fifty-sixes (16 2 ) ‣ 0 four thousand ninety-sixes (16 3 ) � 5

  16. Base 16 (Hexadecimal) Single place has values of 0-15 ‣ Need digits larger than 9. Use A=10, B=11, …, F=15 ‣ In C, starts with a leading 0x or 0X Given a hexadecimal (base 16) number 0x04E5 ‣ 5 ones (16 0 ) ‣ 14 sixteens (16 1 ) ‣ 4 two hundred fifty-sixes (16 2 ) ‣ 0 four thousand ninety-sixes (16 3 ) 16 3 16 2 16 1 16 0 � 5

  17. Base 16 (Hexadecimal) Single place has values of 0-15 ‣ Need digits larger than 9. Use A=10, B=11, …, F=15 ‣ In C, starts with a leading 0x or 0X Given a hexadecimal (base 16) number 0x04E5 ‣ 5 ones (16 0 ) ‣ 14 sixteens (16 1 ) ‣ 4 two hundred fifty-sixes (16 2 ) ‣ 0 four thousand ninety-sixes (16 3 ) 16 3 16 2 16 1 16 0 0 4 E 5 � 5

  18. Base 2 (Binary) � 6

  19. Base 2 (Binary) Only uses the digits 0 and 1 � 6

  20. Base 2 (Binary) Only uses the digits 0 and 1 Given a binary number 0b0000010011100101 ‣ 1 2 0 , 0 2 1 , 1 2 2 , 0 2 3 ‣ 0 2 4 , 1 2 5 , 1 2 6 , 1 2 7 ‣ 0 2 8 , 0 2 9 , 1 2 10 , 0 2 11 ‣ 0 2 12 , 0 2 13 , 0 2 14 , 0 2 15 � 6

  21. Base 2 (Binary) Only uses the digits 0 and 1 Given a binary number 0b0000010011100101 ‣ 1 2 0 , 0 2 1 , 1 2 2 , 0 2 3 ‣ 0 2 4 , 1 2 5 , 1 2 6 , 1 2 7 ‣ 0 2 8 , 0 2 9 , 1 2 10 , 0 2 11 ‣ 0 2 12 , 0 2 13 , 0 2 14 , 0 2 15 2 15..12 2 11..8 2 7..4 2 3..0 � 6

  22. Base 2 (Binary) Only uses the digits 0 and 1 Given a binary number 0b0000010011100101 ‣ 1 2 0 , 0 2 1 , 1 2 2 , 0 2 3 ‣ 0 2 4 , 1 2 5 , 1 2 6 , 1 2 7 ‣ 0 2 8 , 0 2 9 , 1 2 10 , 0 2 11 ‣ 0 2 12 , 0 2 13 , 0 2 14 , 0 2 15 2 15..12 2 11..8 2 7..4 2 3..0 0000 0100 1110 0101 � 6

  23. Converting to decimal � 7

  24. Converting to decimal Multiply and sum up the digit * base position value � 7

  25. Converting to decimal Multiply and sum up the digit * base position value ‣ 1253 = 1*10 3 + 2*10 2 + 5*10 1 + 3*10 0 = 1253 � 7

  26. Converting to decimal Multiply and sum up the digit * base position value ‣ 1253 = 1*10 3 + 2*10 2 + 5*10 1 + 3*10 0 = 1253 ‣ 02345 = 2*8 3 + 3*8 2 + 4*8 1 + 5*8 0 = 1253 � 7

  27. Converting to decimal Multiply and sum up the digit * base position value ‣ 1253 = 1*10 3 + 2*10 2 + 5*10 1 + 3*10 0 = 1253 ‣ 02345 = 2*8 3 + 3*8 2 + 4*8 1 + 5*8 0 = 1253 ‣ 0x04E5 = 0*16 3 + 4*16 2 + 14*16 1 + 5*16 0 = 1253 � 7

  28. Converting to decimal Multiply and sum up the digit * base position value ‣ 1253 = 1*10 3 + 2*10 2 + 5*10 1 + 3*10 0 = 1253 ‣ 02345 = 2*8 3 + 3*8 2 + 4*8 1 + 5*8 0 = 1253 ‣ 0x04E5 = 0*16 3 + 4*16 2 + 14*16 1 + 5*16 0 = 1253 ‣ 0b0000010011100101 = 1253 � 7

  29. Convert the octal value 031 to decimal A. 7 B. 25 C. 31 D. 49 E. 248 � 8

  30. Converting binary to hex Hex Binary Hex Binary 0 0000 8 1000 1 0001 9 1001 2 0010 A 1010 3 0011 B 1011 4 0100 C 1100 5 0101 D 1101 6 0110 E 1110 7 0111 F 1111 � 9

  31. Converting binary to hex Just group digits by 4s starting with LSB Hex Binary Hex Binary 0 0000 8 1000 1 0001 9 1001 2 0010 A 1010 3 0011 B 1011 4 0100 C 1100 5 0101 D 1101 6 0110 E 1110 7 0111 F 1111 � 9

  32. Converting binary to hex Just group digits by 4s starting with LSB Hex Binary Hex Binary ‣ 0b0000010011100101 0 0000 8 1000 1 0001 9 1001 2 0010 A 1010 3 0011 B 1011 4 0100 C 1100 5 0101 D 1101 6 0110 E 1110 7 0111 F 1111 � 9

  33. Converting binary to hex Just group digits by 4s starting with LSB Hex Binary Hex Binary ‣ 0b0000010011100101 0 0000 8 1000 ‣ 0b 0000 0100 1110 0101 1 0001 9 1001 2 0010 A 1010 3 0011 B 1011 4 0100 C 1100 5 0101 D 1101 6 0110 E 1110 7 0111 F 1111 � 9

  34. Converting binary to hex Just group digits by 4s starting with LSB Hex Binary Hex Binary ‣ 0b0000010011100101 0 0000 8 1000 ‣ 0b 0000 0100 1110 0101 1 0001 9 1001 2 0010 A 1010 Each block of 4 bits is 0–15 3 0011 B 1011 4 0100 C 1100 5 0101 D 1101 6 0110 E 1110 7 0111 F 1111 � 9

  35. Converting binary to hex Just group digits by 4s starting with LSB Hex Binary Hex Binary ‣ 0b0000010011100101 0 0000 8 1000 ‣ 0b 0000 0100 1110 0101 1 0001 9 1001 2 0010 A 1010 Each block of 4 bits is 0–15 3 0011 B 1011 ‣ Replace each with a hex digit 4 0100 C 1100 5 0101 D 1101 6 0110 E 1110 7 0111 F 1111 � 9

  36. Converting binary to hex Just group digits by 4s starting with LSB Hex Binary Hex Binary ‣ 0b0000010011100101 0 0000 8 1000 ‣ 0b 0000 0100 1110 0101 1 0001 9 1001 2 0010 A 1010 Each block of 4 bits is 0–15 3 0011 B 1011 ‣ Replace each with a hex digit 4 0100 C 1100 ‣ 0 4 E 5 5 0101 D 1101 6 0110 E 1110 7 0111 F 1111 � 9

  37. Converting binary to hex Just group digits by 4s starting with LSB Hex Binary Hex Binary ‣ 0b0000010011100101 0 0000 8 1000 ‣ 0b 0000 0100 1110 0101 1 0001 9 1001 2 0010 A 1010 Each block of 4 bits is 0–15 3 0011 B 1011 ‣ Replace each with a hex digit 4 0100 C 1100 ‣ 0 4 E 5 5 0101 D 1101 ‣ 0x04E5 6 0110 E 1110 7 0111 F 1111 � 9

  38. Converting binary to octal Octal Binary 0 000 1 001 2 010 3 011 4 100 5 101 6 110 7 111 � 10

  39. Converting binary to octal Just group digits by 3s starting with LSB Octal Binary 0 000 1 001 2 010 3 011 4 100 5 101 6 110 7 111 � 10

  40. Converting binary to octal Just group digits by 3s starting with LSB Octal Binary ‣ 0b0000010011100101 0 000 1 001 2 010 3 011 4 100 5 101 6 110 7 111 � 10

  41. Converting binary to octal Just group digits by 3s starting with LSB Octal Binary ‣ 0b0000010011100101 0 000 ‣ 0b 000 000 010 011 100 101 1 001 2 010 3 011 4 100 5 101 6 110 7 111 � 10

  42. Converting binary to octal Just group digits by 3s starting with LSB Octal Binary ‣ 0b0000010011100101 0 000 ‣ 0b 000 000 010 011 100 101 1 001 2 010 3 011 Each block of 3 bits is 0–7 4 100 5 101 6 110 7 111 � 10

  43. Converting binary to octal Just group digits by 3s starting with LSB Octal Binary ‣ 0b0000010011100101 0 000 ‣ 0b 000 000 010 011 100 101 1 001 2 010 3 011 Each block of 3 bits is 0–7 ‣ Replace each with a octal digit 4 100 5 101 6 110 7 111 � 10

  44. Converting binary to octal Just group digits by 3s starting with LSB Octal Binary ‣ 0b0000010011100101 0 000 ‣ 0b 000 000 010 011 100 101 1 001 2 010 3 011 Each block of 3 bits is 0–7 ‣ Replace each with a octal digit 4 100 ‣ 0 0 2 3 4 5 5 101 6 110 7 111 � 10

  45. Converting binary to octal Just group digits by 3s starting with LSB Octal Binary ‣ 0b0000010011100101 0 000 ‣ 0b 000 000 010 011 100 101 1 001 2 010 3 011 Each block of 3 bits is 0–7 ‣ Replace each with a octal digit 4 100 ‣ 0 0 2 3 4 5 5 101 ‣ 0002345 (We prepended a 0 to denote octal) 6 110 7 111 � 10

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