Binary to Decimal Converter
The Binary to Decimal Converter is a user-friendly online tool, to convert Binary to Decimal quickly.
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Binary to Decimal Converter
Binary to Decimal Converter is just a tool built to make the conversion between numbers represented by only two digits (0 and 1) and the decimal numbers represented by ten digits (0-9). For students, professionals, and enthusiasts working with computers, digital systems, or coding, this tool is incredibly useful – it will make it easy and quick to convert binary numbers into their decimal equivalents.
About Binary and Decimal Number Systems
Binary Number System
The binary system is a base-2 numeral system, meaning it only uses two digits: 0 and 1. In binary numbers each position has a power of 2 starting from
on the right. All modern computing systems exist on this system because digital devices use binary code to process and store data. A binary number is comprised of every bit, or binary digit, representing a single unit of information, either 'on' (1), i.
For example:
Binary number: 1010
Each digit (bit) represents a power of 2:
Decimal Number System
The decimal system is a base-10 numeral system, meaning it uses ten digits: 0 through 9. In daily life, counting, commerce and most math applications use this system. A decimal number contains digits, each of which represents a power of 10 starting from
on the right. Human beings find decimal numbers easier to understand but it is tough when built in digital for binary systems.
For example:
Decimal number: 25
How to convert Binary number to Decimal number
Here, we will write the binary number that we want to convert.
For example, let us use a binary number 1101101.
Here, we will start from the rightmost bit (least significant bit) and raise each bit to the power of 2 moving from right to left. The rightmost bit is 2^0, the next is 2^1, then 2^2, and so on.
Our example using 1101101
2^6 2^5 2^4 2^3 2^2 2^1 2^0
—————————————-
1 1 0 1 1 0 1
We will multiply each bit by its corresponding power of 2 and sum the results.
Using the example 1101101 –
(1 * 2^6) + (1 * 2^5) + (0 * 2^4) + (1 * 2^3) + (1 * 2^2) + (0 * 2^1) + (1 * 2^0)
= 64 + 32 + 0 + 8 + 4 + 0 + 1
= 109
Therefore, the binary number 1101101 is equivalent to the decimal number 109.
Frequently Asked Questions (FAQ)
Q1. What makes computers use binary instead of decimal systems?
A: The fact that there are only two states in a digital circuit means that it can only be 0 meaning the circuit is off or 1, meaning the circuit is on, a simplification that makes the binary easier and more efficient than, for instance, a ten-state system in terms of processing, storing or transmitting in digital gadgets.
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Q2. Now the big question is, any sort of decimal in the binary number?
A: Indeed, it may be done if one uses the binary floating-point format which allows the representation of fractions or decimal points. As with decimal numbers, it is possible to put positions to the left and to the right of the binary point. The binary number 101.1 is represented to 5.5 in decimal.
Q3: Is there a possibility to make a bid from one conversion tool from decimal to binary directly to another conversion tool turning it into a Decimal number without Calculations?
A: Yes! The Binary to Decimal Converter tool mentioned above works in this way for you; just input the binary number to get the converted decimal result. This is important because it does this work for you thereby saving you time, and eliminating chances of making a calculative mistake especially when working with long strings of binary numbers.
Q4: Enumerate a few instances where binary-to-decimal conversion is needed.
A: It is used often in data conversion processes that take place in data processing and networking; COMPUTER PROGRAMMING and COMPUTER HARDWARE ENGINEERING. It helps to learn about error codes and networking IP addresses as well as memory addressing in computer systems.
Q5: To what extent is a binary number able to reach before the conversion tiresomeness sets in?
A: Performing the conversion of binary numbers that are greater than 8 bits or 1 byte will be very time-consuming as well as involving the probability of errors. We can easily convert a binary number of 8 bits, which can still show decimal numbers up to 255, but what about 32b or, indeed 64b, we would use our calculator or a utility tool to do this for us.
Q6: Are there any empirical rules that would help in the conversion between the binary numbers?
A: Yes! Digits in base two, 1, 10, 100, and 1000 in decimal notation are easy to work with since each position in base two counts a power of two. These powers can help to recognize binary values, and here is the list of these powers:
A Table for Binary to Decimal Conversion
| Binary | Decimal |
|---|---|
| 1 | 1 |
| 10 | 2 |
| 11 | 3 |
| 100 | 4 |
| 101 | 5 |
| 111 | 7 |
| 1111 | 15 |
| 11111 | 31 |
| 111111 | 63 |
| 1111111 | 127 |
| 11111111 | 255 |
| 10001000 | 136 |
| 10101010 | 170 |
| 11110000 | 240 |
| 1111101000 | 1000 |