How to Convert Decimal to Hex And Hexadecimal to Decimal Manually
About Decimal (Dec)
- Before you convert decimal to hexadecimal and hex to decimal you must know what are decimal bits and hex bits.
- A decimal or hex bit in this tutorial represents a single number, digit or letter.
- 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.
- Decimal is a number system.
- A decimal number can be represented using a subscript of 10. eg 23510 reads as two hundred and thirty-five base 10.
- These are the numbers we use in every day counting. We mostly use the decimal number system because we have ten fingers.
- The number ten (10) is made by using a combination of two of these decimal numbers: one and zero (1 and 0). While two hundred and nine (209) is a combination of three decimal numbers: two, zero and nine (2, 0 and 9).
- There is no limit as to how many times the numbers can be reused, that is why it is said that numbers are never ending!
About Hexadecimal (Hex)
- Hex is a representation of 4 binary bits
- Hexadecimal, which is also called base 16 or 'hex' for short, consist of sixteen numbers and letters.
- The numbers in hex are the same as decimal numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
- But the big difference between hex and decimal is that hex also contains letters. These letters are: A, B, C, D, E, F.
- A hex number can be represented using a subscript of 16. eg 23516 235 base 16.
- These letters come after its decimal friends in ascending order. Therefore, the Hexadecimal series looks like this: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.
- Hex can be considered as a shorter version of decimal. For example a large number in decimal has a much smaller hex equivalent(using less hex bits to represent the decimal number). I will demonstrate this later.
Hexadecimal to Decimal Conversion
Now how to convert Hex to decimal and decimal to hex manually!
First you must know that the letters in hex all have decimal equivalents, as listed in the table below.
This is a link to another number system table with more values for Octal, Hex, Decimal and Binary. The table below is enough for this tutorial but just in case your were curious I mentioned it.
How to Convert Hex To Decimal!
This is how to convert hexadecimal to decimal manually. You must start by multiplying the hex number by 16. Which will be raised to a power that increases by 1 (the power at which the hexadecimal is raised starts at zero 0), by the hexadecimal number decimal 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. I know this might seen confusing that is why i will provide examples! When converting C9 hexadecimal to decimal your working should look something like this:
9 = 9 * (16 ^ 0) = 9
C = 12 * (16 ^ 1) = 192
We then add the results.
192 + 9 = 20110 decimal.
- First we converted all of our hex numbers to its decimal equivalents. C is equal to decimal 12 (refer to table above) and 9 is equal to decimal 9.
- We then 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.
- Our first multiplication has a power of 0 and the second multiplication has a power of 1. If there was a third it would have a power of 2 and 4 a power of 3 etc....
- The stars (^) in the bracket represent 'raised to the power of'. Therefore, the first terms in brackets read, 'sixteen to the power of 0'. What this means is that sixteen is multiplying by itself zero times. Anything raised to the power of zero is 1. Therefore, 9 is being multiplied by one.
- In the second bracket the terms read as, 'sixteen to the power of one'. A number raised to the power of one is equal to that number. Therefore 12 is being multiplied by 16. When we multiply these we get 192.
- We then added the results in the results column to get our decimal equivalent number. Which is 201.
Convert Hex ABC to decimal
Remember we raise the number sixteen to zero for the rightmost bit of the question. As we move across the numbers and letter in the question the power 16 is raised to is 1 more than the previous bit. For example, if we had a number with 22 bits the leftmost bit would be multiplied by sixteen to the power of 21.
C = 12 * (16 ^ 0) 12
B = 11 * (16 ^ 1) 176
A = 10 * (16 ^ 2) 2560
Answer = 2560 + 176 + 12 = 274810 decimal
Convert Hex AF, ACD, AB2 and FF to base 10
Answers are 17510, 276510, 273810 and 25510 respectively
The subscript at the bottom shows the base
How to Convert Decimal to Hexadecimal Manually
To convert from decimal to hexadecimal you must divide the decimal number by 16 repeatedly. Then write the last remainder you obtained in the hex equivalent column. While doing so, 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 diagram below as an example
Decimal to Hex Result
The answer is C9. As you can see it contains less bits than its decimal equivalent, 201.
- What we did was to divide our decimal number (base 10) by 16 to convert it to a hex equivalent (base 16).
- Our decimal number is 201. 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 is made.
- We then divided our previous answer ,12, by 16. We got a value of zero and a remainder of 12. We then converted 12 to hex. Twelve's hex equivalent 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 respectively.
Convert decimal 3000 to hexadecimal
Divisor Base 10 number Remainder in hex
16 187 remainder 8 = 8
16 11 remainder 11 = B
16 0 remainder 11 = B
Answer equals to BB8 hexadecimal. Remember we write the last remainder we received at the front of our answer
Try these Decimal to Hex Conversions
Convert decimal 39554, 2856, 37 to base 16/Hex
Answers are 9A82, B28 and 25 respectively.
For some, this may seem difficult at first. But rest assured that with a little practice, converting from decimal to hex and changing hex to decimal can easily be mastered. You may check your answers using a calculator, type you decimal value in the dec (may vary depending on calculator) setting and then select 'hex' (may also vary depending on calculator) and press equal. Just do the opposite for hex to decimal. Easy isn't it. Though, I strongly recommend that you learn how to convert these number systems manually before using the calculator. So that you won't have to rely on a calculator to convert them.
An online calculator to convert number systems automatically since you know the basics behind the magic.