Arithmetic For Computer (Number System And Operations) - Integer Arithmetic

The basic arithmetic operations are addition, subtraction, multiplication and division.

Add and Subtract Operation

-Performed in general purpose registers (32 bit).

-2’s complement may generate an overflow.

Instruction syntax :

op 6 bits

rs 5 bits

rt 5 bits

rd 5 bits

sa 5 bits

fn 6 bits

-add up 32-bit word in  rt into the value rs produce result

-rd remain unchanged , Integer Overflow exsception(trap) will occur

Addition:

The rules for binary addition are:

      0         0         1          1

 +    0     +   1     +   0     +    1

      0         1         1        1 0       

* If 1+1, a carry results into the next bit to the left.

Example:

                   1  0  1

     +                1   1

              1  0   0   0           

Subtraction :

Solution 1:

The rules for binary subtraction are:

      0        10         1          1

 -    0     -   1     -   0     -    1

      0         1         1          0      

*If 0-1 , a borrow is required from the right

Example:

              1    0^2 1  0 ² 

          -                1      1

                                   1

Multiplication :

The rules for binary multiplication are:

      0         0         1          1

 X    0     X   1    X    0     X    1

      0         0         0          1       

 Multiplication of two unsigned binary numbers A & B can be

 performed using the longhandalgorithm:

   A:    1 0 1 1

   B:  x   1 0 1

         1 0 1 1

       0 0 0 0

   + 1 0 1 1                                                            .

     1 1 0 1 1 1

the 0 bits in B contribute a 0 to the product, while the 1 bits in B contribute A        shifted left to align with the corresponding bit in B.

Division :

The unsigned binary divisin algorithm is based on longhand algorithm employed for decimal integeers.The dividend is divided by the divisor to obtain the quotient and a remainder.

                5 <--quotient

             ____

divisor--> 2 ) 11 <--dividend

             - 10

             ----

                1 <--remainder

*   If the divisor is larger than the dividend, the quotient is 0 and the remainder equals the dividend.

Otherwise, the divisor is shifted left until the most significant bits of the divisor and dividend are aligned. If the shifted divisor is greater than the dividend, then the resulting quotient bit is 0. Otherwise, the quotient bit is a 1 and the divisor is subtracted from the dividend to produce a remainder. This process is repeated until the remainder from the subtraction is smaller than the divisor.

Hexadecimal Number

- base 16

- present in 4 bit number

Number System Conversion

Decimal	Binary	Hexadecimal
0	0000	0
1	0001	1
2	0010	2
3	0011	3
4	0100	4
5	0101	5
6	0110	6
7	0111	7
8	1000	8

9	1001	9
10	1010	A
11	1011	B
12	1100	C
13	1101	D
14	1110	E
15	1111	F

Hexadecimal Addition
If sum number>1510 ,the amount of sum that exceeds 1610 will carry a 1  to the next column
The hardest additions may be those like D + C. One simple solution is to convert each digit to decimal, add in decimal, and convert the result back to hex (but don't forget to convert it back to hex!)

to add D + C:

convert D to 13

convert C to 12

add 13 + 12 to get 25

convert decimal 25 back to hex 19

Hexadecimal Subtraction

Subtraction that crosses between numbers and letters can be confusing.  For example,

10 - 1 = F

10 - 2 = E

11 - 2 = D

Seeing 10-1, your automatic reaction will be 9, but try to focus on the number system you are using  =]     

                                                                   

CHUAH YIN BOON

B031210335