The decimal and binary number systems are the world’s most commonly utilized number systems presently.
The decimal system, also called the base-10 system, is the system we utilize in our everyday lives. It uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to illustrate numbers. However, the binary system, also called the base-2 system, utilizes only two figures (0 and 1) to portray numbers.
Understanding how to transform from and to the decimal and binary systems are essential for many reasons. For example, computers utilize the binary system to represent data, so software engineers should be expert in converting between the two systems.
Furthermore, learning how to change between the two systems can be beneficial to solve math questions concerning large numbers.
This blog will go through the formula for converting decimal to binary, give a conversion chart, and give instances of decimal to binary conversion.
Formula for Changing Decimal to Binary
The process of converting a decimal number to a binary number is done manually utilizing the following steps:
Divide the decimal number by 2, and note the quotient and the remainder.
Divide the quotient (only) collect in the previous step by 2, and note the quotient and the remainder.
Reiterate the prior steps until the quotient is equivalent to 0.
The binary corresponding of the decimal number is obtained by reversing the sequence of the remainders acquired in the prior steps.
This may sound complicated, so here is an example to illustrate 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 gained by reversing the sequence of remainders (1, 0, 0, 1, 0, 1, 1).
Conversion Table
Here is a conversion chart 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 few examples of decimal to binary transformation using the method talked about priorly:
Example 1: Change 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, that is obtained by reversing 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 equivalent of 128 is 10000000, that is obtained by reversing the sequence of remainders (1, 0, 0, 0, 0, 0, 0, 0).
Although the steps outlined earlier offers a way to manually convert decimal to binary, it can be labor-intensive and error-prone for big numbers. Fortunately, other methods can be utilized to rapidly and simply convert decimals to binary.
For example, you can employ the built-in functions in a calculator or a spreadsheet program to change decimals to binary. You could additionally use online tools such as binary converters, that allow you to enter a decimal number, and the converter will spontaneously produce the corresponding binary number.
It is worth noting that the binary system has handful of limitations compared to the decimal system.
For example, the binary system fails to portray fractions, so it is solely fit for dealing with whole numbers.
The binary system additionally needs more digits to illustrate a number than the decimal system. For example, the decimal number 100 can be illustrated by the binary number 1100100, which has six digits. The length string of 0s and 1s could be inclined to typing errors and reading errors.
Last Thoughts on Decimal to Binary
Despite these restrictions, the binary system has several merits with the decimal system. For instance, the binary system is lot easier than the decimal system, as it just uses two digits. This simplicity makes it simpler to conduct mathematical operations in the binary system, for example addition, subtraction, multiplication, and division.
The binary system is further fitted to representing information in digital systems, such as computers, as it can simply be depicted using electrical signals. As a result, knowledge of how to convert among the decimal and binary systems is important for computer programmers and for unraveling mathematical questions involving huge numbers.
Although the method of changing decimal to binary can be tedious and vulnerable to errors when done manually, there are tools which can rapidly change among the two systems.
