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Here is the one and only guide you need to understand binary!

How does binary work?

  • The binary system is a way of representing data using 0s and 1s. This system is used by computers to represent all the data it works with. To compute a number in this system, you would multiply the digit value by the place value, then add them all together.

How to convert binary to decimal:

  • Step 1: Write the binary number and count the powers of 2 from right to left (starting from 0).

  • Step 2: Write each binary digit(right to left) with corresponding powers of 2 from right to left, such that MSB or the first binary digit will be multiplied by the greatest power of 2.

  • Step 3: Add all the products in the step 2

  • Step 4: The answer is our decimal number.

Here are some examples:




  • Binary is represented in (xxxx)2 and decimal in (xxxx)10 format.





  • Binary numbers are read by separating them into separate digits. Each digit in binary is represented using 0 and 1 and they are the powers of 2 starting from left hand side and then the power is gradually increased from 0 to (n-1).

How to convert decimal to binary:

  • Step 1: Divide the given decimal number by 2, and find the remainder (Ri).

  • Step 2: Now divide the quotient (Qi) that is obtained in the above step by 2, and find the remainder.

  • Step 3: Repeat the above steps 1 and 2, until 0 is obtained as a quotient.

  • Step 4: Write down the remainder in the following manner: the last remainder is written first, followed by the rest in the reverse order (Rn, R(n – 1) …. R1). thus binary conversion of the given decimal number will be obtained.

Here are some examples:




  • The number system that has a base value of 10 is called Decimal Number System. Decimal Numbers are consist of the following digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.





  • All the decimal numbers have their corresponding binary numbers. These binary numbers are used in computer applications and used for programming or coding purposes. This is because binary digits, 0 and 1 are only understood by computers.



Practice your binary conversions here!

Binary to Decimal Converter

Practice your decimal conversions here!

Decimal to Binary Converter

hexadecimal guide (decimal, binary), then add a guessing game that could potentially have all 4 options

How to Convert Decimal to Hexadecimal

  • The hexadecimal number system is a system in which numbers are expressed in the base 16. In the hexadecimal number system, the numbers are represented in terms of 0-9 and A – F. The hexadecimal number is written as number H, (number)16, (number)H. Example: (A23F)16,

  • Step 1: Take the decimal number as dividend and 16 as the divisor (hexadecimal number will have 16 as a base)

  • Step 2: Divide the dividend with the divisor and store the remainder in an array

  • Step 3: Now divide the quotient obtained from the above step by 16 and store the remainder in the array.

  • Step 4: Repeat the third step until the number is greater than zero.

  • Step 5: The final hexadecimal value will be the reverse order of the array.



  • This picture includes an example of a decimal (2545) converted into hexadecimal.





  • This example shows how you can convert into binary and then group to simplify before getting the desired hexadecimal value.

How to Convert Binary to Hexadecimal

  • The Binary to Hexadecimal conversion is the same as above, as you convert from Binary to Hexadecimal in that proccess too!

  • Step 1: Take the decimal number as dividend and 16 as the divisor (hexadecimal number will have 16 as a base)

  • Step 2: Divide the dividend with the divisor and store the remainder in an array

  • Step 3: Now divide the quotient obtained from the above step by 16 and store the remainder in the array.

  • Step 4: Repeat the third step until the number is greater than zero.

  • Step 5: The final hexadecimal value will be the reverse order of the array.





  • This picture shows the exact steps and shows an example of how to convert Binary to Hexadecimal





  • This picture uses the same method, but elaborates the steps more. You can see that it shows the steps (ex. grouping, etc.)

Practice ALL your conversions here!

Bin, Dec, and Hex Converter

Now, apply what you’ve learned and play these guessing games!

Binary to Decimal Guessing Game

Decimal to Binary Guessing Game

The ULTIMATE Binary Game

Binary Conversion Tables

These are all the Binary, Decimal, and Hexadecimal Conversion Tables!

Your Table

Decimal to Binary Table

Decimal Binary
0 0000
1 0001
2 0010
3 0011
4 0100
5 0101
6 0110
7 0111
8 1000
9 1001
10 1010
11 1011
12 1100
13 1101
14 1110
15 1111



Your Table

Your Table

Decimal to Hexadecimal Table

Decimal Digit Hexadecimal Digit
0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
10 A
11 B
12 C
13 D
14 E
15 F


Decimal, Binary, and Hexadecimal Table

Decimal Digit Hexadecimal Digit Binary Form
0 0 0000
1 1 0001
2 2 0010
3 3 0011
4 4 0100
5 5 0101
6 6 0110
7 7 0111
8 8 1000
9 9 1001
10 A 1010
11 B 1011
12 C 1100
13 D 1101
14 E 1110
15 F 1111