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Decimal and binary numbers are commonly used in math and computer science. Decimal numbers are the numbers having two parts: a whole number part and a fractional part. They both are separated by a point. The numbers followed by the point are called decimal numbers. Binary numbers on the other hand are the numbers expressed to the base of 2. Conversion of decimal numbers to the binary formula can be carried out by following certain steps.
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Keywords: Decimal numbers, Binary numbers, conversion formula, base two.
What are Decimal Numbers?
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Decimal numbers are numbers having two parts- a whole number part and a fractional part. They both are separated by a decimal point. The numbers followed by the point are called decimal numbers.
Decimal Number
The decimal numbers are smaller as compared to one. For example, in 10.49, 10 is the whole number, and 49 is the decimal number. Decimal numbers are the fractions expressed in decimal points. Decimal numbers can also be expressed in words, and in expanded forms.
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What are Binary Numbers?
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Binary numbers on the other hand are the numbers expressed to the base of 2. Thus, in this system, the numbers are only expressed in two digits, 0 and 1. Every digit in the binary system is known as the binary digit or bit. Binary numbers are widely used in computers nowadays.
Binary Numbers
| Number | Binary Representation |
|---|---|
| 20 | 0001 |
| 21 | 0010 |
| 22 | 0100 |
| 23 | 1000 |
Decimal To Binary Conversion Formula
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There is no single formula to ensure the conversion, however, there is a stepwise procedure to do the same. The conversion from decimals to binary form is done using the remainder process.
Remainder process: In this process, the number is constantly divided by 2, unless the quotient comes out to be one or zero. During this entire process, the remainders are supposed to be noted.
Remainder Process
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How To Convert A Decimal Number To Binary Formula?
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The process to convert a decimal number to a binary number is laid down below in a stepwise manner:
- The decimal number is first divided by 2, this will give us a quotient and a remainder.
- Note down the remainder, and the quotient obtained is further divided by 2.
- Again, note down the remainder, and the quotient obtained in the second step is again divided by two.
- The above three steps are repeated till the quotient obtained is 0 or 1.
- Now write down the last quotient obtained with the remainders from last to first in the sequence.
- This would give the binary number form of the decimal.
Let us see a few examples to understand the same.
Example 1: Convert 31 to binary digits.
Step 1: The decimal number is firstly divided by 2, this will give us a quotient and a remainder.
31/2 gives quotient 15, remainder 1
Step 2: Note down the remainder, and the quotient obtained is further divided by
15/2 gives quotient 7, remainder 1
Step 3: Again, note down the remainder and the quotient obtained in the second step is again divided by two.
7/2, gives quotient 3, remainder 1
Step 4: The above three steps are repeated till the quotient obtained is 0 or 1.
3/2, gives quotient 1, remainder 1
Step 5: Now write down the last quotient obtained with the remainders from last to first in the sequence.
11111
Step 6: This would give the binary number form of the decimal, 11111.
Example 2: Convert 20 to binary digits.
Solution: 20/2, gives quotient 10, remainder 0
10/2, gives quotient 5, remainder 0
5/2, gives quotient 2, remainder 1
2/2, gives quotient 1, remainder 0
Thus, the binary digits come out to be, 10100
Also Read:
| Real Valued Functions | Complex Numbers and Quadratic Equations |
| Geometric Progression | Arithmetic Progression |
Things to Remember
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- Decimal numbers are the numbers having two parts: a whole number part and a fractional part. They both are separated by a point.
- Binary numbers on the other hand are the numbers expressed to the base of Thus, in this system, the numbers are only expressed in two digits, 0 and 1.
- Conversion of decimal numbers to the binary formula is an exhaustive process and is done by the remainder process.
- Remainder process is the process, where the number is constantly divided by 2 unless the quotient comes out to be one or zero. During this entire process, the remainders are supposed to be noted.
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Sample Questions
Ques: Convert 21 to binary digits. (2 marks)
Ans: 21/2, gives quotient 10, remainder 1
10/2, gives quotient 5, remainder 0
5/2, gives quotient 2, remainder 1
2/2, gives quotient 1, remainder 0
Thus, the binary digits come out to be 10101.
Ques: Convert 30 to binary digits. (2 marks)
Ans: 30/2, gives quotient 15, remainder 0
15/2, gives quotient 7, remainder 1
7/2, gives quotient 3, remainder 1
3/2, gives quotient 1, remainder 1
Thus, the binary digits come out to be, 11110
Ques: Convert 22 to binary digits. (2 marks)
Ans: 22/2, gives quotient 11, remainder 0
11/2, gives quotient 5, remainder 1
5/2, gives quotient 2, remainder 1
2/2, gives quotient 1, remainder 0
Thus, the binary digits come out to be, 10110
Ques: Convert 25 to binary digits. (2 marks)
Ans: 25/2, gives quotient 12, remainder 1
12/2, gives quotient 6, remainder 0
6/2, gives quotient 3, remainder 0
3/2, gives quotient 1, remainder 1
Thus, the binary digits come out to be 11001.
Ques: Convert 29 to binary digits. (2 marks)
Ans: 29/2, gives quotient 19, remainder 1
19/2, gives quotient 9, remainder 1
9/2, gives quotient 4, remainder 1
4/2, gives quotient 2, remainder 0
2/2, gives quotient 1, remainder 0
Thus, the binary digits come out to be 100111.
Ques: Convert 23 to binary digits. (2 marks)
Ans: 23/2, gives quotient 11, remainder 1
11/2, gives quotient 5, remainder 1
5/2, gives quotient 2, remainder 1
2/2, gives quotient 1, remainder 0
Thus, the binary digits come out to be 10111.
Ques: Convert 23 to binary digits. (2 marks)
Ans: 23/2, gives quotient 11, remainder 1
11/2, gives quotient 5, remainder 1
5/2, gives quotient 2, remainder 1
2/2, gives quotient 1, remainder 0
Thus, the binary digits come out to be 10111.
Ques: Convert 33 to binary digits. (2 marks)
Ans: 33/2, gives quotient 16, remainder 1
16/2, gives quotient 8, remainder 0
8/2, gives quotient 4, remainder 0
4/2, gives quotient 2, remainder 0
2/2 gives quotient 1, remainder 0.
Thus, the binary digits come out to be 100001.
Ques: Convert 40 to binary digits. (2 marks)
Ans: 40/2, gives quotient 20, remainder 0
20/2, gives quotient 10, remainder 0
10/2, gives quotient 5, remainder 0
5/2, gives quotient 2, remainder 1
2/2, gives quotient 1, remainder 0
Thus, the binary digits come out to be 101000.
Ques: Convert 43 to binary digits. (2 marks)
Ans: 43/2, gives quotient 21, remainder 1
21/2, gives quotient 10, remainder 1
10/2, gives quotient 5, remainder 0
5/2, gives quotient 2, remainder 1
2/2, gives quotient 1, remainder 0
Thus, the binary digits come out to be, 101011.
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