Binary multiplication is the process of multiplying binary numbers. The process of multiplying binary numbers is the same as that of arithmetic multiplication with decimal numbers. The only difference is that binary multiplication involves numbers that consist of 0s and 1s, whereas, decimal multiplication involves numbers that comprise digits from 0 to 9. Let us learn the process of binary multiplication step by step. To perform a binary multiplication problem, we need to understand how addition works with binary numbers and follow the same process of multiplication and addition we would use with decimal numbers.
Binary Multiplication Table
Since binary numbers make use of only two digits that is 0 and 1, we get to multiply only these binary numbers while performing multiplication. The multiplication table for binary numbers is as follows:
Note that since binary operates in base 2, the multiplication rules we need to remember are those that involve 0 and 1 only. As an example of binary multiplication, we have 101 times 11,
101
× 11
_________
First we multiply 101 by 1, which produces 101. Then we put a 0 as a placeholder as we would in decimal multiplication, and multiply 101 by 1, which produces 101.
101
× 11
_________
101
1010 <-- the 0 here is the placeholder
The next step, as with decimal multiplication, is to add. The results from our previous step indicates that we must add 101 and 1010, the sum of which is 1111.
101
× 11
_________
101
+ 1010
_________
1111
Example: Find the multiplication of (10001)₂ and (101)₂
Solution:
1 0 0 0 1
× 1 0 1
_______________
1 0 0 0 1
+ 1 0 0 0 1 0 0
_______________
1 0 1 0 1 0 1
Answer = 1010101
Example: Find the multiplication of (10101)₂ and (1011)₂
Solution:
1 0 1 0 1
× 1 0 1 1
_______________
1 0 1 0 1
+ 1 0 1 0 1 0
1 0 1 0 1 0 0 0
_______________
1 1 1 0 0 1 1 1
Answer = 11100111
Discussion
Computers don’t multiply in exactly this way, but they do exploit the simplified view of binary multiplication that I’ve described.
Let us take another example with "Logic Kit" app this app is very easy and so good in these subjects of number systems. Download This app from the app store for iOS devices click here.
1- Open the app
2- Choose More Arithmetic
3- Select the base 2
4- write your equation you need to solve
5- You see the solution then click on show steps
Example: Find the multiplication of (1011)₂ and (010)₂
Tags:
Number Systems
