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Understanding CPU Data Types: Integer Real Numbers

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Explore integer, real numbers, character, and boolean data types in CPUs. Learn about memory address, arithmetic operations, and two's complement. Discover how CPUs handle signed and unsigned integers.

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Understanding CPU Data Types: Integer Real Numbers

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  1. CPU Data Types Chapter 3 Integer Real Numbers Character Boolean Memory Address

  2. Integer • Integer • Whole numbers • No decimal places • Unsigned integers • Use entire by ( 8 or 6 bits) for number • Lowest number is zero (0) • Signed integers • Use high order bit for + or – sign • Octal machines have 5 bits for number (out of 6) Excess notation • Hex machines have 7 bit for number (out of 8) Excess notation

  3. Unsigned Signed 32168421-----63 Not counted: used for sign168421-----31 Integer Octal 6 BIT number X X X X X X Weight value 32 16 8 4 2 1 All positions = “1” (“ON”) 1 1 1 1 1 1

  4. Unsigned Signed 1286432168421-----255 Not counted: used for sign6432168421-----127 Integer Hexadecimal 8 BIT number X X X X X X X X Weight value 128 64 32 16 8 4 2 1 All positions = “1” (“ON”) 1 1 1 1 1 1 1 1

  5. Arithmetic Operations Addition Subtraction Multiplication Division

  6. Addition Add two numbers Decimal Binary Binary bit weights 6 0110 1 + 2 + 8 = 1110+ 5 0101 ---- ------- 1110 10112

  7. Subtraction Subtract two numbers Decimal Binary Binary bit weights 6 0110 1 + 0 + 0 + 0 = 110- 5 - 0101 * ---- ------- 110 00002 ? 1 2 3 4 0110-0101 ------- Borrow 1 from2s positionadd to 1s position 0101-0101 ------- Subtract 2s position 0101-0101 -------00 Subtract 1s position 0101-0101 -------0 5 6 7 Answer is: 6- 5----- 0 Subtract 4s position 0101-0101 -------000 Subtract 8s position0101-0101 -------0000

  8. Complements • Binary numbering scheme • Ones (1) become zero (0) • Zeros (0) become ones (1) Octal Hexadecimal 0 000 = 111 0000 = 11111 001 = 110 0001 = 1110 2 010 = 101 0010 = 11013 011 = 100 0011 = 11004 100 = 011 0100 = 10115 101 = 010 0101 = 10106 110 = 001 0110 = 10017 111 = 000 0111 = 10008 1000 = 0111 9 1001 = 0110A 1010 = 0101 B 1011 = 0100 C 1100 = 0011D 1101 = 0010E 1110 = 0001 F 1111 = 0000

  9. Two’s Complement Computers MULTIPLY, SUBTRACT and DIVIDE by ADDITION • Binary numbering scheme • Used to work with negative numbers • Ones (1) become zero (0) • Zeros (0) become ones (1) • Data is signed if: • Variable data type was defined as signed in the program • The number is converted in the program • The computer does a Subtract or Divide • Formula for conversion • Original binary number • Compliment the number • Ones to Zeros • Zeros to Ones • Add binary one to lowest position • High order carry's are discarded

  10. Two’s Complement Add two numbers Decimal Binary Binary bit weights 6 0110 1 + 2 + 8 = 1110+ 5 0101 ---- ------- 1110 10112

  11. Two’s Complement Subtract two numbers Decimal Binary Binary bit weights 1 1 6 0110 1 + 0 + 0 + 0 = 110- 5 +1011 * ---- ------- 110 00012 * Two’s Compliment of 5 5 = 0101 Original Compliment 1010Add one 1 --------Two’s compliment 1011

  12. Summary Computers do Subtraction And Division Using AdditionandTwo’s Compliment

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