# How Do You Convert Binary to Decimal and Vice Versa?

Binary is a two-digit number system composed solely of zeros and ones, commonly utilized by computer engineers, network professionals, and other jobs involving computers.

To convert decimal numbers to binary, divide by 2 and record both the quotient and remainder. Next, double that result before repeating this process until reaching your desired binary number.

Table of Contents

## Basics

As when converting between decimal and binary numbers, binary is a two-digit number system with only zeros and ones, making it very efficient in representing information. Furthermore, binary is widely used across computer engineering, networking and communications applications.

Decimal is an easily understandable number system composed of base-10 numerals that is widely used throughout society and everyday life. People usually convert between decimal and binary using division with remainders as their preferred conversion method.

To convert decimal numbers to binary numbers, begin by dividing each decimal number by 2. Write down both the quotient and remainder, repeat this process until reaching zero division, add up all remaining numbers together for your final binary number and combine.

There are various tools and websites available for converting between decimal and binary numbers, but some of the most popular include calculators, online converters and programming software. To convert between decimal and binary numbers quickly and efficiently, two steps should be followed. First calculate a decimal number’s equivalent in binary by subtracting its smallest value from its largest. Next find its nearest default Value chart value as an equivalent decimal digit and use that result as the initial digit of your binary number.

Step one in converting decimal to binary is starting with the most significant digit (MSB) and working from there. Every time you add another digit, MSB doubles. This method is similar to how computers calculate values.

This method works for any base, so if you need to convert from another number system, simply replace “x 2” with the base of that system (e.g. “octal”, for conversion into decimals, just change “x 2” into “x 37”). For more complex conversions it may be beneficial to keep a reference table handy and refer back to it while making decisions.

## Exponents

The binary number system is one of the simplest forms of number systems. Consisting of just two digits that may either represent 1 or 0, this form of numbering system can easily be implemented into computers and electronic systems due to their lower memory footprint than decimal numbers, as well as being easily convertible back to decimals using either computer software or calculators.

There are various methods available for converting binary numbers to decimals; the easiest and most accurate one is called positional notation. This involves counting each digit of the binary number before multiplying it by the power of 2. It makes this process far less laborious than trying to count entire whole numbers individually and provides greater precision than simply counting whole numbers by eye.

Another way of converting binary numbers is the doubling method, which is less complex but harder to keep track of in your head than positional notation. Simply write out your binary number that needs to be converted, divide by 2 and add its quotient to each binary digit that represents it – then “flip” all these digits until all their equivalent decimal digits exist – eventually you should end up with a decimal equivalent that equals its binary counterpart!

To convert a binary floating point number to decimal format, start by dividing it by its base number system base and then by 2. Divide that second number in half again before adding it back onto your first multiplied number. This method makes processing integral and fractional parts of numbers separately easier; write down both integer parts that you added onto the mantissa before writing down their decimal equivalent if more than one needs converting at a time. If necessary repeat this process until all numbers have been transformed to decimal.

## Powers of 2

Converting binary to decimal is usually accomplished by multiplying and adding. But for large numbers like 138, using a table of powers of 2 can make the conversion simpler. You would start by performing repeated divisions by 2 while keeping track of any remainders, then sum up all values in reverse order until you reached your binary number.

In essence, this method resembles using a calculator; however, for beginners it may be more complex to grasp.

When converting decimal to binary, one key aspect to keep in mind is that numbers may only consist of either one or zero digits – unlike decimals which allow up to 10 digits.

At first glance, it may make sense that the easiest way to convert numbers to binary is by performing repeated division by two. This will yield a quotient of one every time and make keeping track of remainders simpler; this technique is commonly known as double-dabble method.

Next, remember that every digit of a binary number can only represent either zero or one. A bit is the smallest unit of information within a computer system and must either be one or zero in binary coding. The most significant bit corresponds with the first digit in a number and the least significant with its last.

When converting decimal to binary numbers, one alternative method used for conversion is called the doubling method. Although more complicated than its counterpart, it still makes for easy work when working with larger numbers. This works by multiplying each binary digit by two before adding it onto its decimal number counterpart.

## Tables

The binary number system is the basic level of data encoding, consisting of eight bits representing either 1 or 0. Each bit represents either 1 or 0, so all 8 bits together hold 16 values; computers find this system easier to work with; it also makes conversion from binary numbers into decimals easy as all you need to do is add up the digits.

If you are working with long binary numbers, it can be useful to use an online binary converter as a quick and easy way to check your work. These websites can also come in handy when writing computer programs that need to convert between these numeral systems – simply enter the binary number into their respective boxes before clicking “Convert” or “Calculate” button and get back a decimal answer!

Convert binary to decimal with ease by using a table, where the first digit in each cell of the table represents 1. It follows with 2, then 3, 4 and 5, thus producing five-digit binary numbers like 1000010010. This method works better if you are familiar with both decimal and binary number order.

Another method for converting binary numbers to decimals is multiplying them with their appropriate base number. This process resembles that used when converting fractions; you must begin by taking note of both integer and decimal parts before dividing by 2 with taking note of both quotient and remainder values, then repeat until your quotient reaches 0. Finally, write down any remainders in reverse order.

If you are dealing with short binary numbers, this step may not be necessary. Most people find this approach to be faster than using tables; its main benefit being not having to memorize powers of 2. Furthermore, using manual conversion can serve as an excellent test to see if your answer was accurate.