The decimal and binary number systems are the world’s most commonly utilized number systems today.
The decimal system, also known as the base-10 system, is the system we use in our everyday lives. It utilizes ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to portray numbers. However, the binary system, also known as the base-2 system, uses only two figures (0 and 1) to depict numbers.
Learning how to transform from and to the decimal and binary systems are vital for multiple reasons. For instance, computers use the binary system to portray data, so software engineers are supposed to be competent in converting between the two systems.
Furthermore, understanding how to change between the two systems can help solve math problems including large numbers.
This blog article will cover the formula for changing decimal to binary, provide a conversion table, and give examples of decimal to binary conversion.
Formula for Changing Decimal to Binary
The process of changing a decimal number to a binary number is performed manually utilizing the ensuing steps:
Divide the decimal number by 2, and note the quotient and the remainder.
Divide the quotient (only) found in the prior step by 2, and record the quotient and the remainder.
Repeat the prior steps until the quotient is equal to 0.
The binary corresponding of the decimal number is achieved by reversing the series of the remainders received in the prior steps.
This might sound confusing, so here is an example to illustrate this process:
Let’s change the decimal number 75 to binary.
75 / 2 = 37 R 1
37 / 2 = 18 R 1
18 / 2 = 9 R 0
9 / 2 = 4 R 1
4 / 2 = 2 R 0
2 / 2 = 1 R 0
1 / 2 = 0 R 1
The binary equal of 75 is 1001011, which is gained by reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion table depicting the decimal and binary equivalents of common numbers:
Decimal | Binary |
0 | 0 |
1 | 1 |
2 | 10 |
3 | 11 |
4 | 100 |
5 | 101 |
6 | 110 |
7 | 111 |
8 | 1000 |
9 | 1001 |
10 | 1010 |
Examples of Decimal to Binary Conversion
Here are some instances of decimal to binary conversion using the steps discussed priorly:
Example 1: Convert the decimal number 25 to binary.
25 / 2 = 12 R 1
12 / 2 = 6 R 0
6 / 2 = 3 R 0
3 / 2 = 1 R 1
1 / 2 = 0 R 1
The binary equal of 25 is 11001, which is acquired by inverting the sequence of remainders (1, 1, 0, 0, 1).
Example 2: Change the decimal number 128 to binary.
128 / 2 = 64 R 0
64 / 2 = 32 R 0
32 / 2 = 16 R 0
16 / 2 = 8 R 0
8 / 2 = 4 R 0
4 / 2 = 2 R 0
2 / 2 = 1 R 0
1 / 2 = 0 R 1
The binary equal of 128 is 10000000, which is acquired by reversing the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Although the steps defined earlier provide a method to manually change decimal to binary, it can be time-consuming and error-prone for large numbers. Luckily, other ways can be employed to rapidly and effortlessly change decimals to binary.
For example, you can use the built-in functions in a spreadsheet or a calculator application to convert decimals to binary. You could further utilize online tools for instance binary converters, which allow you to enter a decimal number, and the converter will automatically produce the equivalent binary number.
It is worth noting that the binary system has handful of constraints in comparison to the decimal system.
For instance, the binary system is unable to illustrate fractions, so it is solely fit for representing whole numbers.
The binary system further requires more digits to illustrate a number than the decimal system. For example, the decimal number 100 can be portrayed by the binary number 1100100, which has six digits. The extended string of 0s and 1s can be liable to typing errors and reading errors.
Final Thoughts on Decimal to Binary
Regardless these limitations, the binary system has a lot of merits with the decimal system. For instance, the binary system is lot easier than the decimal system, as it only utilizes two digits. This simplicity makes it simpler to perform mathematical functions in the binary system, for instance addition, subtraction, multiplication, and division.
The binary system is more suited to representing information in digital systems, such as computers, as it can effortlessly be represented utilizing electrical signals. As a result, understanding how to change among the decimal and binary systems is crucial for computer programmers and for solving mathematical problems including large numbers.
Although the method of changing decimal to binary can be labor-intensive and vulnerable to errors when done manually, there are tools which can quickly change between the two systems.
