All Arithmatic operations using Bitwise operators only

[Aftabpasha]

Is it possible to perform all arithmetic operations (+,-,*,/) using Bitwise operations only. Please consider signed numbers also.
Thank You.

[weaknessforcats]

Of course. That's how the processor does it.

[Aftabpasha]

@weaknessforcat s

Yes, I have a method for addition and subtraction given below

int add(int a, int b)
{ 
           do
           {
                      a=a^b;
                      b=(a^b)&b;
                      b=b<<1;
           } while(b);
 
           return(a);
}
 

Basically using this method, one can perform Multiplication and Division operations.
Now, is there any other specialized methods for Multiplication and Division operations? e.g. (num<<1) is like (num*2) and (num>>2) is same as (num/2).
Here we are not using the addition or subtraction operations, but directly obtaining results of Multiplication and Division operations. Please explain any such method.
Please give example of processors methods of these operations(+,-,*,/).
Thank You.

[weaknessforcats]

I don't see a question in your reply. In any case, I cannot provide solutions, act as a tutor or do research for you.

Please read the posting guidelines.

[Bassem]

Hi Aftabpasha,

It is true that you can perform all arithmetic operations using the two basics operations + and -.
I have studied Z80 Microprocessor by mad by Zilog, it offers only ADD, SUB, INC (increment), and DEC (decrement) arithmetical operations (beside Logic operations), we typed programs in assembly to make Multiplication and Division, and what amazing is that it still produced and successes until now in many new and complicated applications.


the next Microprocessor generation 8086 provides MUL and DIV operations, and an improvement in H/W (Hardware) like increasing the addressing capacity, data bus 16 bit and pipelining etc.


But nowadays CPUs with high Memory capacity and provide very complex operations like Log, antiLog, tan, cos, .... and that is what you use in home and me and everyone else.

[Bassem]

Here is Example


Multiplication of two numbers

int MULT(int x, int y)
{
int n = x;
while (n) {
x += y;
n--;
}
return y;
}

Division of two numbers

int DIV(int x, int y)
{
int n = 0;
while (x > y) {
x -= y;
n++;
}
return n; // truncate fraction
}

[donbock]

Is this assignment for a programming class or a Boolean algebra course? You should start with addition: google the term "half adder". You can add two binary numbers by stringing together enough half adders. Once you have addition working it is simple to get subtraction: google the term "two's complement". Multiplication is repeated addition; division is repeated subtraction.

[Bassem]

I worked on a personal Microprocessor Simulator last year, where i used basic logic gates (AND, OR, XOR) to perform all mathematical operations provided by the MP using Boolean to represent data in registers.

Introduce a big piece of code may confuse or tiered, so i expected these methods to declare the way of thinking, not to explain the whole idea.

Regards

[JosAH]

@Bassem
Don't do it that way; it takes ages to complete; the Russian Peasant Method is more clever:

int mul(int x, int y) {
   int p;
   for (p= 0; x; x>>= 1, y<<= 1)
      if (x&1) p+= y;
   return p;
}
 

kind regards,

Jos

[Banfa]

Bassem, your multiplication algorithm is wrong you return y which is unchanged by the function.

Everyone, you are left shifting a signed value. For C (and I assume C++ but I don't actually know) this is a platform defined operation, that is different platforms may implement it differently producing different results (normally depending of whether the platform performs an arithmetic or logical shift).

For portability it is only safe to shift unsigned values.