Numeral system conversion


This is website where you can convert any number from one numeral system to another.
For example you can convert Binary to Decimal or Binary to Hexadecimal or Hexadecimal to Binary. In fact you can convert any Numeral system to any other Numeral system. We accept more that 30 base systems. Our website is easy to use. Just write number choose numeral system and our website will convert your number to more that 30 other numeral systems. For example if you put binary number it will be converted to Decimal, Hexadecimal, Octal and all others...
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Insert number and choose numeral system of Your Inserted Number and our website will convert it to another numeral systems.









Binary to Decimal

Binary numbers are easy to calculate and perform numerical computation. A computer understands binary numbers which are in form of bits of 0 and 1 and performs all the arithmetic and logical calculations using these binary digits. We though decipher numbers in decimal format a computer understands binary therefore a computer converts decimal numbers to binary and then perform the calculations and then again the binary results are converted to decimal for the user to understand and interpret.
There are various methods through which we can convert a binary number to decimal yet the most simple format or method is by placing the decimal numbers in a table which corresponds to the binary equivalent. To elaborate a table is drawn from left to right in the form of power of digit 2 starting with 1. So the right most column of the table has the digit 1 and then to its left the digit 2 then follows 4, 8, 16, 32, and 64 and so on and so forth.
Just beneath this decimal number table we then place the binary numbers. The decimal number which corresponds to 1 is written separately and the decimal number which corresponds to 0 is dropped. Then the total of all the decimal numbers is made to finally find the decimal number for the binary digit.
Let us further explain this with an example.
Say we have to convert a binary digit 10001110 into decimal.

For this conversion first we would place all the binary digits into a table.

1286432168421
10001110

So here we observe that first we begin from the extreme right of the binary digit 10001110 and we take 0 and place it to the extreme right of the table corresponding to 1. Then we take the next binary digit 1 and place it corresponding to 2, and then we again take 1 and place it beneath 4 and continue this sequence till we place the beginning digit of the binary and place it corresponding to 128.
Now the next step would be to consider all those decimal numbers which correspond to 1 of the binary digit series.
In this example the decimal numbers which correspond to binary digits are;
128, 8, 4 and 2.
Rest all the numbers correspond to binary 0 so we do not consider them.
Now to find the binary equivalent of the binary digit 10001110, we would finally add the four decimal numbers we selected from the conversion table.
128+8+4+2 = 142
So it can be finally deduced that the binary equivalent of 10001110 will be 142.
Thus it is very clear from this example that to convert a binary digit into a decimal number format is very simple and convenient. All the user has to do is to place the binary number into the conversion table and ascertain the value for each binary digit. The decimal number which corresponds to 1 is selected and the decimal number which corresponds to 0 is dropped.

Decimal to Binary

The numeric system that we use in general is known as the Decimal System. The decimal system uses 10 as its base. The number 10 is used as the base, since any given number is a combination of digits ranging from 0 to 9 (10 digits). The value of the digits is assigned as per their relative position in the number. This place value increases in the multiples of 10 as we go from right hand side towards the left. Hence, every digit can be represented as a multiple of 10 with an appropriate power. As a general rule, any number with the power of 0 is always 1. For example, the number 5269 can be represented as:
(5×103) + (2×102) + (6×101) + (9×100) = 5269

As we can see in the above example, each digit is multiplied by 10 and assigned an appropriate power according to its position in the number which increases as we go from right towards left. As the base is 10 for Decimal Numbers, similarly the base is 2 for the Binary system. The Binary system uses only ‘1′ or ‘0′ to represent all numbers. Since we use only ‘1′ and ‘0′ (two digits), 2 acts as the base for binary numbers. The concept of place value in the binary system is very similar to that of Decimal system. The place value of digits in a number increases as we go from right towards left. The value of each digit is twice that of its previous digit but is represented only by ‘1′ or ‘0′. Let us consider the following illustration:

Decimal Digit Value2561286432168421
Binary Digit Value101001001


We don’t need to consider the values represented by 0. We will only add up the values represented by 1. So, the equation is:
256 + 64 + 8 + 1 = 32910

From the above illustration, we understand that the number 1010010012 (binary number) is equivalent to 32910 in the decimal system. When binary number system is used in computers or the digital system, ‘1′ represents ‘ON’ and ‘0′ represents ‘OFF’.

Let us consider the following example where the decimal number 240 is converted into its binary number equivalent.

Number 240 Whenever a number is Divided by “2″, a result and a remainder are derived. MSB represents the most significant bit and LSB represents least significant bit. The binary number is derived going forward from MSB towards LSB.
divide by 2
result 120 remainder 0 (LSB)
divide by 2
result 60 remainder 0
divide by 2
result 30 remainder 0
divide by 2
result 15 remainder 0
divide by 2
result 7 remainder 1
divide by 2
result 3 remainder 1
divide by 2
result 1 remainder 1
divide by 2
result 0 remainder 1 (MSB)


So, when we move from MSB towards LSB i.e. from bottom to upwards, the binary number formed is 11110000. The binary number 111100002 is equivalent to the 24010 decimal number.



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