1.To do binary ,multiplicate we have
4 rules we should follow in binary multiplication as in table:
Table
3.1.This is The Binary Number operations Rules :
|
Binary
Rules
|
Multiply
|
|
0 x 0 = 0
|
0
|
|
0
x 1 = 1
|
0
|
|
1
x 0 = 1
|
0
|
|
1
x 1 = 1
|
1
|
.
Binary
Multiplication
Binary multiplication uses the same
algorithm, but uses just three order-independent facts: 0 x 0 = 0, 1 x 0 = 0,
and 1 x 1 = 1 (these work the same as in decimal). If you perform the
multiplication phase with these facts, you’ll notice two things: there are
never any carries, and the partial products will either be zeros or a shifted
copy of the multiplicand.
Observing this, you’ll realize
there’s no need for digit-by-digit multiplication, which means there’s no need
to consult a times table — which means there’s no multiplication, period!
Instead, you just write down 0 when the current digit of the multiplier is 0,
and you write down the multiplicand when the current digit of the multiplier is
1.
In the introduction, I showed this
example: 1011.01 x 110.1. I wrote it as if you followed the decimal algorithm
to the letter. Here’s how it looks if you follow the simpler “write zero or
multiplicand” algorithm (it’s the same result, but with blanks representing 0s;
this matches better conceptually with what we are now doing):
Firstly to do the multiplication we must use the table 3.1 to do the Binary
Number Operations Rules.
Here’s what the “multiplication”
phase looks like, step-by-step:
Steps of Binary Multiplication
(Multiplication Phase Only)
Each step is the placement of an
entire partial product, unlike in decimal, where each step is a single-digit
multiplication (and possible addition of a carry).
In the addition phase, the partial
products are added using binary
addition, and then the radix point is placed
appropriately. This gives the answer 1001001.001.
Decimal Multiplication
To multiply two multiple-digit decimal numbers, you first need to know how to multiply two single-digit decimal numbers. This requires the memorization of 100 facts, or 55 facts if you exclude the commutative or “turnaround” facts. These facts are usually represented in a “multiplication table,” also known as a “times table.” Example facts are 2 x 9 = 18, 9 x 7 = 63, and 1 x 6 = 6.A multiplication problem is written with one number on top, called the multiplicand, and one number on the bottom, called the multiplier. The algorithm has two phases: the multiplication phase, where you produce what are called partial products, and the addition phase, where you add the partial products to get the result.
In the multiplication phase, the digits of the multiplier are stepped through one at a time, from right to left. Each digit of the multiplicand is then multiplied, in turn, by the current multiplier digit; taken together, these single-digit multiplications form a partial product. The answer to each single-digit multiplication comes from the multiplication table. Some of these answers are double-digit numbers, in which case the least significant digit is recorded and the most significant digit is carried over to be added to the result of the next single-digit multiplication.
For example, let’s multiply 3.87 and 5.3:
Example of Decimal Multiplication
Steps of Decimal Multiplication (Multiplication Phase Only)
This is step how to do the multipication.
