Thomaset2000’s Room

Hi! I want to share a method to easily convert a decimal number into binary number and vice versa. I learned this method of converting decimal to binary while I was studying for my C1003 Mathematics for Computing.

The Basic Concept

The basic concept of this method is looking at the fact that we just need to add one zero each time we multiply the decimal equivalent of a binary number by 2 (two).

Let me give an example:

The binary equivalent for decimal number 2 is 10 (one zero), then if we multiply the 2 with 2 we will get 4 (2*2 = 4), the binary equivalent of 4 is 100 (one zero zero).

Let’s take a look at the table below

The table above shows the equivalence of six decimal number with the binary number. You can see that if we multiply the decimal number by two then we will get the same binary number with one extra zero e.g. two is equal to one zero and four is equal to one zero zero. From this simple concept, we can convert decimal to binary and binary to decimal easily.

Decimal to Binary Conversion

First, let us try to apply the basic concept above to convert decimal number into binary number. Let see at the following example:

Convert decimal number 20 (twenty) into binary

To convert twenty into binary let us look at the table that we make earlier

Then we try to make 20 (twenty) from the decimal numbers that we found in our table above. Since we have 1, 2, 4, 8, 16, and 32 the best way to make 20 is to add 4 and 16 since 4 + 16 = 20.
So we take 4 and 16 from the table, 4 is equal to 100 (one zero zero) and 16 is equal to 10000 (one zero zero zero zero). The final step is to add these two binary number and make it looks like this :
20 = 4 + 16 = 100 + 10000 = 10100 (one zero one zero zero)
So, in the end we get that decimal number 20 = 10100 (one zero one zero zero) in binary number.

Binary to Decimal Conversion

Now, we are going to look on how we apply our simple concept to convert a binary number into decimal number. Let us consider the following example :

Convert binary number 10101 (one zero one zero one) into decimal number

To convert this binary number, we still use our table

From this table, we will break the binary 10101 like this:
10101 = 10000 + 100 + 1

So we get that 10101 consist of 10000, 100, and 1. Then lets look at the table, we will get this:

10101 = 10000 + 100 + 1 = 16 + 4 + 1 = 21 (twenty one, a decimal number)

Yes thats all! simple isn’t it??

Do you have any comment on this? maybe you have something to ask me or want to discuss with me about this?
Feel free to use the comment box below (click here if you cannot see the comment box).

admin Education, IDIC, Informatics Binary, binary conversion, binary to decimal conversion, C1003, decimal to binary conversion, Mathematics for Computing