How to convert a number into binary format ?

Asked 08-Feb-2019
Updated 30-Mar-2023
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An easy method of converting decimal to binary number equivalents is to write down the decimal number.


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Converting a number into binary format is a process of expressing the number in terms of 0s and 1s. Binary format is a representation of a number in the base 2 system, rather than the more commonly used base 10 system. This system is made up of two digits, 0 and 1, which represent off and on states, respectively.

In order to convert a number into binary format, you must first determine the value of each binary digit. This is done by raising the base (2) to a power. For example, the rightmost binary digit ( digit 1) is the same as 2^0, the second digit (digit 2) is 2^1, the third digit (digit 3) is 2^2, and so on.

How to convert a number into binary format

Once you have determined the value of each binary digit, you must then determine the value of the number you are trying to convert. To do this, you must add up the values of each binary digit, multiplied by the number that the binary digit represents. For example, if you have a binary number of 1011, the value of the number would be 1*2^3 + 0*2^2 + 1*2^1 + 1*2^0, which equals 11.

To convert a number into binary, you can also use a process called division by two. This process involves starting with the number you wish to convert and then dividing it by two. You will then record the remainder (either 0 or 1) and the quotient (the result of the division). You will then repeat the process with the quotient until the quotient is 0. The sequence of remainders that you record is what makes up the binary representation of the number.

For example, if you are trying to convert the number 11 into binary format, you would start by dividing 11 by 2, which would give you a quotient of 5 and a remainder of 1. You would then divide 5 by 2, which would give you a quotient of 2 and a remainder of 1. You would then divide 2 by 2, which would give you a quotient of 1 and a remainder of 0. Finally, you would divide 1 by 2, which would give you a quotient of 0 and a remainder of 1. The sequence of remainders that you record is 1,1,0,1, which is the binary representation of 11.

In summary, converting a number into binary format is a process of expressing the number in terms of 0s and 1s. It involves determining the value of each binary digit by raising the base (2) to a power, and then adding up the values of each binary digit, multiplied by the number that the binary digit represents. You can also use a process called division by two to convert a number into binary, by starting with the number you wish to convert, and then dividing it by two, and recording the remainders until the quotient is 0.