Binary Multiplication:We know there are four fundamental operations in arithmetic, addition, subtraction,
multiplication and division. We have already discussed about the binary addition and binary
subtraction in detail in the previous articles now we are going to discuss about binary
multiplication in a detailed manner. As in binary number system there are only 0 & 1 present
as digits so we have to know the fundamental interrelation between these two digits during
multiplication. Like in case of binary addition and binary multiplication there are also four
steps to be followed during a bigger multiplication or we can say these fundamental steps as
well. These are
0
*
0
1
*
0
0
*
1
1 * 1 = 1 (there is no carry or borrow for this)
=
=
=
0
0
0
As we can see that if we can compare these rules of binary multiplication with that of decimal
multiplication we will not have any difference at all. So it is a comparatively easy method
than
the
previously
discussed
two
operations.
Now we will look into the procedure in a more detailed matter and step by step to understand
it better.
Let us take two binary numbers A = 1001 and B = 101 we want to find out A * B
This is the first step in this step the least significant bit or the right most bit of B is multiplied
with all the digits of A from the right side and the result is written.
Here the steps took place are 1 * 1 = 1, 1 * 0 = 0, 1 * 0 = 0, 1 * 1 = 1.
Similarly in this step all the elements of A are respectively multiplied with the second most
significant bit i.e. 0. From the table above we can see that any digit 0 or 1 when multiplied by
0, the result is 0 so all the elements in this step is 0. Now we will proceed to the next step.
In this step the left most digit of B which is 1 is multiplied by all the digits of A and the result
is same as that of the first step.
Finally all these elements are added and we ultimately get the desired result of binary
multiplication. If we look carefully the binary addition method is applied here which is very
simple to understand.
Binary Division:Finally we will discuss the last part of binary arithmetic which is last but not the least in
detail i.e. binary division. Division is also a very important part of arithmetic which cannot be
ignored at all. Now coming to division process it is perhaps the most difficult part to
understand of all the binary arithmetic operations. Though it is not too much difficult, it may
look a bit tougher than the other binary operations because all the other had some similarity
among themselves like they all had four basic steps which made all the processes quiet easy
to understand but the binary division process does not have any specific rule to follow.
Though this process is quite similar to the decimal division. The process will not be clear
until we look at an example.
Let us take A = 11010 and B = 101
We want to divide A by B
The structure of operation of binary division is similar to that of decimal division, now we
will look into the operation step by step to make it understanding as much as possible.
In the first step the left most digits of dividend i.e. A are considered and depending upon the
value the divisor is multiplied with 1 and the result which is the result of multiplication of
101 and 1 are written. As we already know that 1 * 1 = 1, 1 * 0 = 0 and 1 * 1 = 1 that is
exactly what is written.
In this step 101 is subtracted from 110. This step is also very easy to understand as we
already know binary subtraction method. Now going into the next step.
As of the rules of division the next least significant bit comes down and we try to multiply 1
with divider i.e. B but the result is bigger than the minuend so this step cannot be completed
and we have to go to the next step.
0 is inserted into the quotient and the least significant bit comes down now we can proceed to
the next step.
Now again the divisor is multiplied with 1 and the result is written, the result is similar to the
first one because all the numbers are same. Now we are going into the final step.
In the final step binary subtraction is done and we get the remainder and the operation of
binary
division
is
completed
and
we
get
the
following
result.
Quotient = 101 and remainder = 1.