Topic 1 Subtopic 4: Basic Binary Number Operation

A binary number operation will be focusing only in addition, subtraction, multiplication and division.

Binary Addition

Adding binary numbers is a simple task and very similar to the addition of decimal numbers. As with decimal numbers, you start by adding the bits (digits) one column, or place weight, at a time, from right to left. Unlike decimal addition, there is little to memorize in the way of rules for the addition of binary bits:

0 + 0 = 0
1 + 0 = 1
0 + 1 = 1
1 + 1 = 10
1 + 1 + 1 = 11

  

Adding two binary numbers together is like adding decimal numbers, except 1 + 1 = 10 (in binary), so you have to carry the one to the next column:


  0001
+ 0100
  ----
  0101

  0001
+ 0001 
  ----
  0010 (1 plus 1 is 10,carry the 1 to the next column)
  0011
+ 0011 
  ----
  0110 (1 + 1 = 10, so carry; then 1 + 1 + 1 = 11, so carry again)

  0011
+ 0101 
  ----
  1000 (carry in every column here)




Binary Subtraction

Work the columns from right to left subtracting in each column. If must subtract a one from a zero, you need to borrow from the left , just as in decimal subtraction.


* 1011011 − 10010 = 1001001:






1
0
1
1
0
1
1
−
1
0
0
1
0
1
0
0
1
0
0
1




*  00100101 − 00010001 = 00010100:

           

            0
      0  0  1 10  0  1  0  1  
    - 0  0  0  1  0  0  0  1
      0  0  0  1  0  1  0  0

 * 00110011 − 00010110 = 00011101:

              0 10  1


       0  0  1  1  0 10  1  1
  


     - 0  0  0  1  0  1  1  0



       0  0  0  1  1  1  0  1







Binary Multiplication
Binary multiplication uses the same technique as decimal multiplication. In fact, binary multiplication is much more easy because each digit we multiply by is either zero or one. Multiplication is achieved by adding a list of shifted multiplicands according to the digits of the multiplier.


* 1011 x 1101 = 10001111:


                                    1 0 1 1
                 x  1 1 0 1

                             -------------

                                   1 0 1 1 

                                0 0 0 0 

                             1 0 1 1 

                          1 0 1 1 

                       -----------------

                      1 0 0 0 1 1 1 1    

   

* 1011.01 x 110.1 = 1001001.001:


                                 1 0 1 1.0 1

                        x             1 1 0.1

                          ------------------

                                1 0 1 1 0 1

                             0 0 0 0 0 0

                          1 0 1 1 0 1

                       1 0 1 1 0 1

                    ----------------------

                    1 0 0 1 0 0 1.0 0 1  


   

Binary Division



Binary division is the repeated process of subtraction, just as in decimal division.

*  100010010 ÷ 1101 = 000010101: 






                     _
*  1011.11 ÷  11 = 11.1110:
                             _
                                                                    1 1 . 1 1 1 0      
                             1 1 ) 1 0 1 1 . 1 1 0 0 0
                                -    1 1
                                            1 0 1
                                            -  1 1
                                                1 0  1
                                                -  1  1 
                                                    1  0 1
                                                   -    1 1  
                                                         1 0 0
                                                        -   1 1
                                                                1 0 0     --->  Repeated

Goh Menning              B031210149