Binary to Decimal

How to use this Binary to Decimal Converter by Myfavetools

This binary to decimal translator lets you turn binary number to decimal without any extra requirements. You can use Myfavetools binary to decimal conversion tool on every operating system or device without stress.

To start with this tool,  follow the steps given below:

• Enter your binary digits either by copying and pasting from your file, uploading file from your computer or by typing yourself.
• Proceed by clicking on the "Convert to decimal" button, and the results will be displayed below the convert binary to decimal online conversion tool.
• You can copy the results by clicking on the “Copy to clipboard” button or you can highlight all the text, right click and select the copy option from the menu and paste it in your desired location, you can also download and save a txt file to your computer.

Binary to Decimal Conversion Table

How to Convert Binary to Decimal

A number system is a method of representing numbers in mathematics. There are four different sorts of number systems, including:

Binary Number System (Base – 2) 
Octal Number System (Base – 8)
Decimal Number System (Base – 10)
Hexadecimal Number System (Base – 16)
All computer hardware, but especially computer architecture, heavily relies on the number system. Computer engineers, communication experts, networking experts, and other professions use it. Let's first gain an understanding of both number systems before moving on to the binary to decimal conversion.

What is a Binary Number System?

The simplest type of number system, known as a binary number system, only uses the numbers 0 (zero) and 1. (one). The base 2-numerical system is another name for it. Electronic gadgets and computer architecture primarily employ this number.

Binary number system examples include 01, 101, 1110, 10011, 1011101, and so forth.

What is a Decimal Number System?

Numbers 0 through 9 are represented via a decimal number system. The most prevalent number system in use by the general public is the decimal one. The base-10 numeral system is another name for these numbering schemes.

Decimal number system examples include 10, 121, 485, 8483, 82940, and so forth.

What is the conversion of binary to decimal?

The base 2 numeral system is turned into the base 10 numeral system when the binary number system is translated to the decimal number system. Because computer programming uses binary to decimal conversion, it is crucial to know. Thus, whereas humans can readily understand the decimal number system, which has all ten digits, a machine can only understand the binary number system, which is represented by the numbers 0 and 1. Therefore, learning how to translate between binary and decimal number systems is crucial.

Decimal to Binary Conversion Techniques

To translate binary number systems into decimal number systems, there are two basic approaches. These approaches are:

• Positional Notation
• Conversion Using Doubling 

Positional Notation

Write the binary number and, beginning at 0, count the powers of 2 from right to left.
Starting from right to left, each binary number now gets its associated power of 2. Thus, the bit with the highest power of 2 will be the most important one. 
Add the outcome of the subsequent step.
The final response will be transformed into a base-10 decimal number.

Examples:

• (10001)2

1    0    0     0     1 = 1 x 24 + 0 x 23 + 0 x 22 + 0 x 21 + 1 x 20 = 16 + 0 + 0 + 0 + 1 = (17)10

• (1000.101)2

1    0    0     0   .   1   0    1 = (1 x 23 + 0 x 22 + 0 x 21 + 0 x 20) . (1 x 2-1 + 0 x 2-2 + 1 x 2-3) = (8 + 0 + 0) . (0.5 + 0 + 0.125) = (8.625)10

Conversion Using Doubling

One of the simplest methods for turning binary integers into decimal numbers is via doubling. We must select the number's leftmost or most significant bit. The result is then stored after being multiplied by 2, added, and the second-leftmost bit. In a similar manner, we must multiply the outcome by two, then take the third leftmost bit and update the outcome. This procedure will be carried out until we reach the rightmost portion, which is the least important bit. Doubling is the term used to describe this operation because we are multiplying by 2. 

Examples:

• (10011)2

1   0     0    1    1 = 1 = 1 x 2 + 0 = 2 = 2 x 2 + 0 = 4 = 4 x 2 + 1 = 9 = 9 x 2 + 1 = 19 = (19)10

• (10000101)2

1   0   0   0   0   1   0   1 = 1 = 1 x 2 + 0 = 2 = 2 x 2 + 0 = 4 = 4 x 2 + 0 = 8 = 8 x 2 + 0 = 16 = 16 x 2 + 1 = 33 = 33 x 2 + 0 = 66 = 66 x 2 + 1 = 133 = (133)10

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