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Hex to Decimal or Binary to Decimal Easy Conversion

Converting Hexadecimal  to decimal takes effort, Although, Converting hexadecimal to binary is very easy, that’s why hexadecimal has been used in some programming languages.  but once you get it then it’s easy to change those tricky numbers and letters to something you or your computer can understand. Let’s understand Hexadecimal Basics first.

01. How to use Hexadecimal?

Our conventional decimal counting system is base ten, utilizing ten unique symbols to show numbers. Hexadecimal is a base sixteen number system, which means it utilizes sixteen characters to show numbers.

Below there’s a hexadecimal chart to help you convert hex to decimal easily. This hexadecimal table is quite helpful in converting hex to decimal values and also known as hex translator.

  • Counting from zero upward:
Hexadecimal Decimal
0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
A 10
B 11
C 12
D 13
E 14
F 15
10 16
11 17
12 18
13 19
14 20
15 21
16 22
17 23
18 24
19 25
1A 26
1B 27
1C 28
1D 29

02. Use Subscript to show which system you’re using:

At whatever point it may be unclear which system you’re utilizing, utilize a decimal subscript number to mean the base. For instance, 1710 means “17 in base ten” (a conventional decimal number). 1710 = 1116, or “11 in base sixteen” (hexadecimal). You can skip this if your number has an alphabetic character in it, for example, B or E. Nobody will mix up that for a decimal number.

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Convert Hex to Binary

What are Binary Numbers?

In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically 0 (zero) and 1 (one). The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices.

01. Convert each Hexadecimal digit to four Binary digits.

Hexadecimal was accepted in any case since it’s so natural to change over between the two. Basically, hexadecimal is utilized as an approach to show binary data in a shorter string. This table is all you have to change over from one to the other:

Below there’s a binary chart to help you convert hex to binary easily. This binary table is quite helpful in converting hex to binary values and also known as binary translator.

Hexadecimal Binary
0 0000
1 0001
2 0010
3 0011
4 0100
5 0101
6 0110
7 0111
8 1000
9 1001
A 1010
B 1011
C 1100
D 1101
E 1110
F 1111

It really is as simple as changing the digit into the four equivalent binary digits.

Let’s Understand How this works. In the “base two” binary system, n binary digits can be used to represent 2n different numbers. For example, with four binary digits, you can represent 24 = 16 different numbers. Since hexadecimal is a base sixteen system, a one digit number can be used to represent 161 = 16 different numbers. This makes conversion between the two systems extremely easy.

  • You can also think of this as the counting systems “flipping over” to another digit at the same time. Hexadecimal counts “…D, E, F, 10” at the same time binary counts “1101, 1110, 1111, 10000“.

Hexadecimal to Binary is a trivial conversion. Each hexadecimal digit can be directly converted to its four bit binary equivalent, using this table if necessary.

For example the hex number FACE16 can be converted by converting F to 1111, A to 1010, C to 1100 and E to 1110. The binary number is then simply 1111101011001110.

Convert Hexadecimal to Decimal

01. Review how base ten works. You utilize decimal documentation consistently without stopping and consider the importance, however when you initially learned it, your parent or instructor may have disclosed it to you in more detail. A speedy survey of how normal numbers are composed will enable you to change over the number:

  • Each digit in a decimal number is in a certain “place.” Moving from right to left, there’s the “ones place,” “tens place,” “hundreds place,” and so on. The digit 3 just means 3 if it’s in the ones place, but it represents 30 when located in the tens place, and 300 in the hundreds place.
  • To put it mathematically, the “places” represent 100, 101, 102, and so on. This is why this system is called “base ten,” or “decimal” after the Latin word for “tenth.”

02. Write a decimal number as an addition problem. This will probably seem obvious, but it’s the same process we’ll use to convert a hexadecimal number, so it’s a good starting point. Let’s rewrite the number 480,13710. (Remember, the subscript 10 tells us the number is written in base ten.):

  • Starting with the rightmost digit, 7 = 7 x 100, or 7 x 1
  • Moving left, 3 = 3 x 101, or 3 x 10
  • Repeating for all digits, we get 480,137 = 4x100,000 + 8x10,000 + 0x1,000 + 1x100 + 3x10 + 7x1.

03. Write the place values next to a hexadecimal number. Since hexadecimal is base sixteen, the “place values” compare to the powers of sixteen. To change over to decimal, multiply each place value by the relating power of sixteen. Begin this procedure by composing the powers of sixteen alongside the digits of a hexadecimal number. We’ll do this for the hexadecimal number C92116. Start on the right with 160, and increase the exponent each time you move left to the next digit:

  • 116 = 1 x 160 = 1 x 1 (All numbers are in decimal except where noted.)
  • 216 = 2 x 161 = 2 x 16
  • 916 = 9 x 162 = 9 x 256
  • C = C x 163 = C x 4096

04. Convert alphabetic characters to decimal. Numerical digits are the same in decimal or hexadecimal, so you don’t need to change them (for instance, 716 = 710). For alphabetic characters, refer to this list to change them to the decimal equivalent:

  • A = 10
  • B = 11
  • C = 12 (We’ll use this on our example from above.)
  • D = 13
  • E = 14
  • F = 15

05. Perform the calculation. As everything is written in decimal now, do each multiplication problem and add the results together. A calculator will help for most hexadecimal numbers. Continuing our example from earlier, here’s C921 rewritten as a decimal formula and solved:

  • C92116 = (in decimal) (1 x 1) + (2 x 16) + (9 x 256) + (12 x 4096)
  • = 1 + 32 + 2,304 + 49,152.
  • 51,48910. The decimal version will usually have more digits than the hexadecimal version, since hexadecimal can store more information per digit.

Convert Hex to Binary or Decimal Video

If you still didn’t get it, here’s the video to help you do so.

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