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Chapter 1
DATA REPRESENTATION
Complements

Examples                  Examples
   10’s C                    1’s C
    • 512790 = 487210          • 011100 = 100011
    • 14672.3 = 85327.7
                              2’s C
   7’s C                      • 010101 = 101011
    • 65172 = 12605
                              16’s C
                               • 59A1D = A65E3
Systems Used to Represent Negative Numbers

Signed-Magnitude Representation
    A number consists of a magnitude and a symbol
     indicating whether the magnitude is positive or
     negative.

Examples:
     +85 = 010101012           -85 = 110101012
     +127 = 011111112          -127 = 111111112
Systems Used to Represent Negative Numbers


Signed-Complement System
• This system negates a number by taking its
  complement as defined by the system.

Examples:
  +85 = 010101012           -85 = 101010102 (1s)
  +127 = 011111112          -127 = 100000012 (2s)
Chapter 2

COMPUTER ARITHMETIC
Arithmetic in various Number Systems

• Addition of numbers in any number system
  – Add numbers starting at the least significant
    digit.
  – Perform addition on numbers of the same
    number base.
• Subtraction of numbers
  – Must use complements
Binary Addition

• To add binary numbers: (X + Y)
   – Get the SCR of the negative numbers
   – Add the two numbers
   – If the SCR used is:
      • 2's C: Discard end carry
      • 1's C: Add the end carry to the sum
Example: Binary Addition

• Add the following numbers. Use 8 bits to
  represent each number.
  – 6 + 13
  – 6 + (-13)
  – (-6) + 13
  – (-6) + (-13)
Example: Binary Addition


•   6 + 13 = 19
Example: Binary Addition


•   6 + 13 = 19
    0 0000110
Example: Binary Addition


•   6 + 13 = 19
    0 0000110
+   0 0001101
Example: Binary Addition


•   6 + 13 = 19
    0 0000110
+   0 0001101
=   0 0010011
Example: Binary Addition


•   6 + 13 = 19   •   6 + (-13) = -7
    0 0000110           0 0000110
+   0 0001101
=   0 0010011
Example: Binary Addition


•   6 + 13 = 19   •   6 + (-13) = -7
    0 0000110           0 0000110
+   0 0001101                          (1's)
=   0 0010011
Example: Binary Addition


•   6 + 13 = 19   •       6 + (-13) = -7
    0 0000110               0 0000110
+   0 0001101         +     1 1110010 (1's)
=   0 0010011
Example: Binary Addition


•   6 + 13 = 19   •       6 + (-13) = -7
    0 0000110               0 0000110
+   0 0001101         +     1 1110010 (1's)
=   0 0010011         =     1 1111000
Example: Binary Addition


 • (-6) + 13 = 7
                (2's)




6 = 0 0000110
Example: Binary Addition


 • (-6) + 13 = 7
    1 1111010 (2's)




6 = 0 0000110
Example: Binary Addition


 • (-6) + 13 = 7
   1 1111010 (2's)
 + 0 0001101



6 = 0 0000110
Example: Binary Addition


 • (-6) + 13 = 7
   1 1111010 (2's)
 + 0 0001101
 =10 0000111


6 = 0 0000110
Example: Binary Addition


 • (-6) + 13 = 7
   1 1111010 (2's)
 + 0 0001101
 =10 0000111


6 = 0 0000110
Example: Binary Addition


 • (-6) + 13 = 7     •   (-6) + (-13) = -19
   1 1111010 (2's)         1 1111010 (2's)
 + 0 0001101
 =10 0000111


6 = 0 0000110
Example: Binary Addition


 • (-6) + 13 = 7     •       (-6) + (-13) = -19
   1 1111010 (2's)             1 1111010 (2's)
 + 0 0001101             +     1 1110011 (2's)
 =10 0000111


6 = 0 0000110
Example: Binary Addition


 • (-6) + 13 = 7     •     (-6) + (-13) = -19
   1 1111010 (2's)          1 1111010 (2's)
 + 0 0001101             + 1 1110011 (2's)
 =10 0000111             = 11 1101101


6 = 0 0000110
Example: Binary Addition


 • (-6) + 13 = 7     •     (-6) + (-13) = -19
   1 1111010 (2's)          1 1111010 (2's)
 + 0 0001101             + 1 1110011 (2's)
 =10 0000111             = 11 1101101


6 = 0 0000110
Examples: Addition

• (999.5 + 281.6)10
        1 1 1

        999.5
  +     281.6
       1 281.1
Examples: Addition

• (999.5 + 281.6)10   • (110.11 + 101010.11)2
        1 1 1                 1 1 1   1   1

        999.5                  110.11
  +     281.6          +    101010.11
       1 281.1              1100 01.10
Examples: Addition

• (355.45 + 240.664)8

   355.45
 + 240.664
 =
Examples: Addition

• (355.45 + 240.664)8
         1

   355.45
 + 240.664
 =           4
Examples: Addition

• (355.45 + 240.664)8
         1

   355.45
 + 240.664
 =        34
Examples: Addition

• (355.45 + 240.664)8
        1   1

   355.45
 + 240.664
 =     6.3 34
Examples: Addition

• (355.45 + 240.664)8
     1   1   1

   355.45
 + 240.664
 = 6 16.3 3 4
Examples: Addition

• (355.45 + 240.664)8   • (A0C.D + E72.9)16
      1   1   1

   355.45                      A0C.D
 + 240.664               +     E72.9
 = 6 16.3 3 4            =
Examples: Addition

• (355.45 + 240.664)8   • (A0C.D + E72.9)16
      1   1   1                   1

   355.45                      A0C.D
 + 240.664               +     E72.9
 = 6 16.3 3 4            =         .6
Examples: Addition

• (355.45 + 240.664)8   • (A0C.D + E72.9)16
      1   1   1                    1

   355.45                      A0C.D
 + 240.664               +     E72.9
 = 6 16.3 3 4            =   1 8 7 F.6

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DIFFERENT BASKETRY IN THE PHILIPPINES PPT.pptx
 

Chapter2a