Number Operation

NUMBER OPERATION

The four main number operations in binary number is addition, subtraction, multiplication and division.

BINARY ADDITION

Rules of Binary Addition

	Sum	Carry
0 + 0 = 0	0	0
0 + 1 = 1	1	0
1 + 0 = 1	1	0
1 + 1 = 1	0	1

Example:

  1.     100011 + 000101 = 101000

           1 1 1  =  carries

  1 0 0 0 1 1  =  35(base 10)
+0 0 0 1 0 1  =  5  (base 10)
__________
  1 0 1 0 0 0  =  40 (base 10)

        2. 01011001 + 01101101 = 11000110

                                                        1   1 1       1    = carries
                                                   0 1 0 1 1 0 0 1 =   89( base 10)
                                                + 0 1 1 0 1 1 0 1 = 109(base 10)
                                                _____________
                                                   1 1 0 0 0 1 1 0 = 198(base 10)

        

       3.   11000.11 + 11.11 = 11100.10

                                                             1 1 1  1    = carries
                                                   1 1 0 0 0. 1 1 = 24.75 (base 10)
                                              +           1 1. 1 1 = 3.75  (base 10)
                                           ______________
                                                   1 1 1 0 0. 1 0 = 28.50 (base 10)

Two’s Compliment Addition

Example:

-15 + 10 = 1111 0001 + 0000 1010
              =  1111 1011

1^st step:  Change -15 into 2^nd complement number
            binary number for -15 : 0000 1111
             1^st complement : 1111 0000
             2^nd complement : 1111 0001

2^nd step: Add them together
                                       
                             1 1 1 1 0 0 0 1 =  -15 (base 10 )
                           +0 0 0 0 1 0 1 0 = +10 (base 10)
                          ______________
                             1 1 1 1 1 0 1 1  = -5 (base 10)

Overflow will occur when two 2^nd complement’s number is add together with same sign (both  positive and both negative). Overflow never occurs when adding operands with different signs.

The situation below will occur overflow:

 (+A) + (+B) = - C
 (-A)  + (-B) = + C   

Example:  -5 + -3 = -8
                       

                                    1 0 1 1
                                 + 1 1 0 1
                               ________
              overflow ---- 1 1 0 0 0

BINARY SUBTRACTION

Rules of Binary Subtraction

	Sum	Borrow
0 – 0 = 0	0	0
0 – 1 = 1	1	10
1 – 0 = 1	1	0
1 – 1 = 1	0	1

Two’s Compliment Subtraction

Overflow occurs when 2 two’s complement numbers with different sign is subtracted.

The situation below will occur overflow:
(+A) – (- B) =  -C
(- A) – (+ B) = +C

BINARY MULTIPLICATION

Rules of Multiplication

	Multiply
0 x 0 = 0	0
0 x 1 = 0	0
1 x 0 = 0	0
1 x 1 = 1	1

BINARY DIVISION

Written by:

Name：Woon Pei Wen,Loo Shi Min

No.Matrik : B031210273,B031210106