The decimal and binary number systems are the world’s most frequently used number systems right now.
The decimal system, also called 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 represent numbers. However, the binary system, also called the base-2 system, uses only two figures (0 and 1) to depict numbers.
Learning how to convert between the decimal and binary systems are important for many reasons. For instance, computers utilize the binary system to represent data, so software engineers must be proficient in converting within the two systems.
In addition, comprehending how to change within the two systems can helpful to solve mathematical problems including large numbers.
This blog will go through the formula for transforming decimal to binary, provide a conversion table, and give instances of decimal to binary conversion.
Formula for Changing Decimal to Binary
The method of changing a decimal number to a binary number is done manually using the following steps:
Divide the decimal number by 2, and record the quotient and the remainder.
Divide the quotient (only) obtained in the prior step by 2, and note the quotient and the remainder.
Repeat the previous steps unless the quotient is equivalent to 0.
The binary corresponding of the decimal number is obtained by inverting the sequence of the remainders acquired in the prior steps.
This might sound confusing, so here is an example to show you this process:
Let’s convert 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 acquired by reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion table portraying 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 examples of decimal to binary transformation employing the steps talked about earlier:
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 equivalent of 25 is 11001, that is acquired by reversing the series of remainders (1, 1, 0, 0, 1).
Example 2: Convert 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 equivalent of 128 is 10000000, which is obtained by reversing the invert of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Although the steps described prior provide a method to manually convert decimal to binary, it can be tedious and prone to error for big numbers. Thankfully, other systems can be utilized to rapidly and effortlessly convert decimals to binary.
For instance, you could use the incorporated functions in a calculator or a spreadsheet program to change decimals to binary. You can also use web tools similar to binary converters, that enables you to input a decimal number, and the converter will spontaneously produce the corresponding binary number.
It is worth pointing out that the binary system has some limitations contrast to the decimal system.
For example, the binary system cannot portray fractions, so it is only suitable for dealing with whole numbers.
The binary system also requires more digits to illustrate a number than the decimal system. For instance, the decimal number 100 can be portrayed by the binary number 1100100, that has six digits. The long string of 0s and 1s could be inclined to typos and reading errors.
Last Thoughts on Decimal to Binary
Regardless these restrictions, the binary system has some advantages with the decimal system. For instance, the binary system is much simpler than the decimal system, as it just uses two digits. This simplicity makes it easier to perform mathematical functions in the binary system, for example addition, subtraction, multiplication, and division.
The binary system is more suited to representing information in digital systems, such as computers, as it can easily be depicted using electrical signals. Consequently, knowledge of how to convert among the decimal and binary systems is crucial for computer programmers and for unraveling mathematical problems concerning large numbers.
Although the process of changing decimal to binary can be labor-intensive and prone with error when done manually, there are tools that can easily convert among the two systems.
