# Convert Hex To Binary Manually Turning A Breech I'm an online writer and car enthusiast with years of car maintenance experience. Before you convert a decimal to a hexadecimal and a hexadecimal to a decimal you must know what decimal bits and hex bits are.

First, a decimal or hex bit in this tutorial represents a single number, digit, or letter. A decimal is also called base 10 and denary because it consists of ten numbers. These are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

## ALPHABET IN HEXADECIMAL AND BINARY, CAPITAL LETTERS

A decimal is a number system and can be represented using a subscript of 10 i. Decimals are the numbers we use in everyday counting. We mostly use the decimal number system because we have ten fingers. The number 10 is made by using a combination of two of these decimal numbers: 1 and 0 while a number like is a combination of three decimal numbers: 2, 0, and 9. There is no limit as to how many times the numbers can be reused, that's why it is often said that numbers are never ending.

A hexadecimal, which is also called base 16 or "hex" for short, is a representation of four binary bits and consists of sixteen numbers and letters. The numbers in a hex are the same as decimal numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

The big difference between a hex and a decimal is that a hex also contains letters. A hex number can be represented using a subscript of 16 i. These letters come after the decimals in ascending order.

A hex can be considered a shorter version of a decimal. For example a large number in decimal form has a much smaller hex equivalent using less hex bits to represent the decimal number. I will demonstrate this later. Now, how do you convert a hex to a decimal and a decimal to a hex manually? First, you must know the letters in a hex all have decimal equivalents, as listed in the table below.

There are other number system table with more values for octals, hexes, decimals, and binaries, however the table below provides all that we need for this tutorial. To convert a hexadecimal to a decimal manually, you must start by multiplying the hex number by Then, you raise it to a power of 0 and increase that power by 1 each time according to the hexadecimal number equivalent. We start from the right of the hexadecimal number and go to the left when applying the powers. Each time you multiply a number by 16, the power of 16 increases.

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Remember that we raise the number 16 to 0 for the rightmost bit of the question. As we move across the numbers and letters, the power 16 is raised by one more than the previous bit. For example, if we had a number with 22 in the leftmost bit it would be multiplied by 16 to the power of Answers are 10 , 10 , 10 , and 10 respectively. To convert from decimal to hexadecimal you must divide the decimal number by 16 repeatedly.

## Decimal, the Base 10 Numbering System

Then, write the last remainder you obtained in the hex equivalent column. If the remainder is more than nine, remember to change it to its hex letter equivalent. The answer is taken from the last remainder obtained. Refer to the diagram below as an example:.

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The answer is BB8 hexadecimal. Remember, we write the last remainder we received at the front of our answer. For some, this may seem difficult at first.

But rest assured that with a little practice, converting from a decimal to a hexadecimal and a hexadecimal to a decimal can be easily mastered. It may help you to check your answers using a calculator, or to type your decimal value in the dec setting and then select "hex" and press equal. Just do the opposite for hex to decimal. Another option is using a decimal to hexadecimal converter or a hexadecimal to decimal converter.

Still, I strongly recommend you learn how to convert these number systems manually before using the calculator. That way, you won't feel that you need to rely on a calculator. Sign in or sign up and post using a HubPages Network account.

Comments are not for promoting your articles or other sites. Thank you! I found some parts of this quite hard to understand, like the remainders and how to do it without a calculator. Please help me to understand, my maths isn't that good with division. To get the remainder of 9, like in the example, you need to take the remainder. Converting is a two step process, yet for some reason no one ever mentions this, hope this helps someone! Other product and company names shown may be trademarks of their respective owners.

## Binary, Decimal, Hex, the Manual way!!

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## Hexadecimal to Binary and Binary to Hexa Conversion

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## Hex to Binary converter

What Is a Hexadecimal? Converting a Hexadecimal to a Decimal Now, how do you convert a hex to a decimal and a decimal to a hex manually?

Hexadecimal to Decimal Table Hexadecimal. Then, we add the results. C is equal to decimal 12 refer to table above and 9 is equal to decimal 9.

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Then, we multiplied the numbers 12 and 9 starting from the last number in the question by 16 and its power. Remember, the powers start from zero.

## Convert hex to binary manually turning a breech

Our first multiplication had a power of 0 and the second multiplication had a power of 1. If there was a third it would have had a power of 2. Anything raised to the power of zero is 1. Therefore, 9 was multiplied by one. In the second bracket, the term read, "16 to the power of 1. Therefore 12 was multiplied by When we multiplied these we got We then added the results to get our decimal equivalent number, which was Example 2 In this example, we want to convert hex ABC to a decimal.

Test Yourself! Refer to the diagram below as an example: Example 1. Thus, the answer is C9.

## How to Convert Hex to Binary and Binary to Hexadecimal

As you can see, it contains less bits than its decimal equivalent, Review We divided our decimal number base 10 by 16 to convert it to a hex equivalent base Our decimal number was We divided this by 16 to get a value of 12 with a remainder of 9. The hex equivalent for 9 is 9 so no change was made. We then divided our previous answer, 12, by We got a value of zero and a remainder of We then converted 12 to hex. The hex equivalent of 12 is C refer to the first table.

We then wrote our answer from the last remainder we received to the first in the order from left to right. Example 2 In this example, we want to convert decimal to a hexadecimal. Answers are 9A82, B28, and 25 respectively. Conclusion For some, this may seem difficult at first. Questions must be on-topic, written with proper grammar usage, and understandable to a wide audience. It was a very helpful. Thanks for your easy way to understand these You are correct Alex.

It was my mistake sorry for the trouble. I've found most sites do not mention what you need to do with the remainder. Sign In Join. Connect with us. This website uses cookies As a user in the EEA, your approval is needed on a few things. This is used to identify particular browsers or devices when the access the service, and is used for security reasons.