CONT....ARITHMETIC FOR COMPUTER

THIS POST IS CONTINUITY FROM PREVIOUS POST....

BASIC BINARY NUMBER OPERATIONS

A binary number operation include addition, subtraction, multiplication and division. The fundamental explorations on computer binary number operations will be more exciting if we used and understanding the basic  of number calculation between human and computer. Come and lets learn how computer will do the calculation.

• ADDITION

• SUBTRACTION

• MULTIPLICATION

• DIVISION

Before doing the all operation we should know the RULES ….

BINARY ADDITION…

Here are the simple rules in binary addition ops….

 there are 4 rules that should be follow when doing this

                                                  TABLE 1-BINARY NUMBER OPERATION RULES

BINARY RULES	SUM	CARRY
0 + 0 = 0	0	0
0 + 1 = 1	1	0
1 + 0 = 1	1	0
1 + 1 = 1	0	1

EXAMPLE:  BY USING FOURTH RULES…

                                                                         

                                                                CARRY                  1    1

                                                                                                0     1      1

                                                                                          +    0     0      1

                                                                                                1     0      0   SUM 

BINARY SUBTRACTION…         

Let’s  proceed with another 4 rules in  binary subtraction ops….

TABLE 2- BINARY NUMBER OPERATION RULES

BINARY RULES	SUM	BORROW
0 – 0 = 0	0	0
0 – 1 = 1	1	10
1 – 0 = 1	1	0
1 – 1 = 1	0	1

EXAMPLE:

      a)      11 – 10                                        

     solution;                                                   

                1 1                                                         

-   0 1

                1 0

      b)    101 – 011

solution;

(left column : when a 1 is borrowed , a 0 is left , so 0-0=0)

0            1 (middle column: borrow 1 from next column to the left , making a 10 in this column,then 10-1=1 )

                   1         0        1

                -  0         1        1

                   0         1        0

BINARY MULTIPLICATION…

Next, 4 rules that should be follow when doing binary multiplication ops…

TABLE 3 – BINARY NUMBER OPERATIONS RULES

BINARY RULES	MULTIPLY
0 X 0 = 0	0
0 X 1 = 1	0
1 X 0 = 1	0
1 X 1 = 1	1

EXAMPLE : Multiply the binary numbers 1010 and 1001

                1010
             x 1001
                1010
              0000
            0000
          1010        
          1011010

BINARY DIVISION...

For your information , binary division follow the same rule as binary multiplication

   

HEXADECIMAL NUMBER OPERATION...

1) Hexadecimal Addition

2) Hexadecimal Subtraction

let me show what is hexadecimal addition ops is...

In hexadecimal addition , if the sum number is greater than 15₁₀ ,  the amount of the sum that exceeds 16₁₀ will carry a 1 to the next column….

Example: 

a) 58₁₆ + 22_{16                                    b)}  2 B₁₆ + 84_{16                            c)}  DF₁₆ + AC₁₆

solution :

a)  
           5       816
       +  2       216
           7     1016     = 7A16            




b)
           2        B16
       +  8        416 
              10      1516      =  AF16



c)                                                       D           F

                                                                            +     A            C

                        13₁₀   +   10₁₀    +   1₁₀   =  24₁₀         15₁₀     +    12₁₀     =    27₁₀

                                          24₁₀    -   16₁₀   =  8₁₀            27₁₀      -    16₁₀    =   11₁₀

                                                                          =  8₁₀                                                 =    B₁₀  (with a 1 carry)
                                                          (with a 1 carry)               

                                                     

                                                          

answer :  18B

prepared by: Nurul Izzati Nor Rusham (B031310238)