The decimal number system is the same one we use on a daily basis. We employ decimals while dealing with money matters, determining distances, measuring the worth of products and during arithmetic computations. However, it’s the binary system that is utilized by computers since there are only two digits involved – zero and one – and the binary system represents numbers and other kinds of data stored in digital devices.
If you’re a beginner learner, understanding decimal to binary conversions would become a necessary skill, which might sound difficult to you but actually it’s too easy with certain steps and practice.
What Exactly is Decimal?
The decimal number system is also referred to as the base-10 numeral system since it employs ten digits, namely, zero till nine.
A position in a decimal number represents the power of ten. For instance, the decimal 245 can be put forth as-
245 = 2 × 100 + 4 × 10 + 5 × 1
Thus
245 = 200 + 40 + 5.
This place value system seems simple for people to comprehend and utilize.
And what’s a Binary number?
Binary is actually a base-2 numeral system where only two digits are used instead of ten:
0 and 1.
Each place in a binary number corresponds to the powers of two starting from right to left like-
1, 2, 4, 8, 16, 32, 64, 128 and so on.
Consider the binary 1011
This is expandable as-
1 × 8 + 0 × 4 + 1 × 2 + 1 × 1
this gives:
8 + 0 + 2 + 1 = 11
Hence, 1011 in binary is 11 in decimal.
How to convert it to binary from decimal?
You must have come across so many methods, but the division by 2 method is too easy when converting a whole decimal number to binary.
Keep dividing by 2 and writing down the remainder each time. Continue doing this until the quotient has become zero and then read the recorded remainders from bottom to top.
Let’s convert a few numbers for proper understanding;
Example 1: Convert 10 to binary
Divide 10 by 2 to begin with-
10 ÷ 2 = 5 remainder 0
Now,
5 ÷ 2 = 2 remainder 1
Next,
2 ÷ 2 = 1 remainder 0
Finally,
1 ÷ 2 = 0 remainder 1
And finally, read from bottom to top-
1010
Hence, 10 in decimal is equivalent to 1010 in binary. We can now check the answer using place values:
1010 = 1 × 8 + 0 × 4 + 1 × 2 + 0 × 1
= 8 + 2
= 10
So the answer is definitely correct.
Example 2: Convert 13 to binary
Keep repeating step 1 with the number 13-
13 ÷ 2 = 6 remainder 1
Then,
6 ÷ 2 = 3 remainder 0
Next,
3 ÷ 2 = 1 remainder 1
Finally,
1 ÷ 2 = 0 remainder 1
Hence, read from bottom to top-
1101
And thus, 13 in decimal is equivalent to 1101 in binary. Check using place values again:
1101 = 1 × 8 + 1 × 4 + 0 × 2 + 1 × 1
= 8 + 4 + 1
= 13.
Example 3: Convert 25 to binary
Let’s try a bigger number and convert it:
25 ÷ 2 = 12 remainder 1
12 ÷ 2 = 6 remainder 0
6 ÷ 2 = 3 remainder 0
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
Reading remainders from bottom to top we’ve:
11001
Hence, 25 in decimal is equivalent to 11001 in binary. Let’s put it up to check-
11001 = 1 × 16 + 1 × 8 + 0 × 4 + 0 × 2 + 1 × 1
= 16 + 8 + 1
= 25.
Alternative method: using powers of 2
Another basic method to convert a decimal number into a binary number would be to find out powers of 2 which add up to the decimal number and hence determine a binary value. Let’s find out the binary representation for decimal 18.
Powers of 2 are: 1, 2, 4, 8, 16, 32 and so on.
To sum 18, we require:
16 + 2 = 18.
So for 16 we will place a 1, then 0 for 8, 0 for 4, 1 for 2, and 0 for 1, hence,
10010.
Thus, 18 in decimal is equivalent to 10010 in binary.
This method is useful as it helps you know what particular position in a binary number represents.
Some errors made by beginners
There are a few errors commonly made by students when they are converting decimal numbers into binary numbers. Reading the remainders in the wrong order is one, then forgetting remainders (which have a value of 0 or 1), not continuing until the quotient has reached zero or incorrectly remembering what an equivalent place value represents. They mix them up; 10 is not the same as 2, but binary 10 is 2. In binary numbers, any position represented in place value stands for some power of 2 instead of 10.
Importance of decimal to binary conversion
Understanding decimal to binary conversion helps people understand how computers store different kinds of information. The values such as 0 or 1 each stand for 1 bit, which helps computers process information. Other subjects like digital logic, computer architecture or binary computation can also be understood.
When you need to check a conversion or work with different number-system values, a Binary Converter can also be useful for getting a quick result while learning the manual process.
What a user could think at the end of the session?
Converting decimal to binary can be seen as a task which depends on a few rules in the division method where numbers continue to get divided by 2 and recording the remainder each time until the quotient becomes zero and then reading remainders from bottom to top and hence obtaining binary values like:
10 = 1010, 13 = 1101, 18 = 10010, 25 = 11001, as demonstrated above using these binary values, this conversion task may seem much fun.