How to Convert Denary to Binary

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Denary is the number system we use everyday, which is more popularly known as the decimal system. Binary is the number system used in computers and electronics. There are 10 digits in denary: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9; there are only two bits (or binary digits) in binary: 0 and 1. These are simpler to transmit and easily represents the on or off state. An on state is represented by 1 and an off state is represented by 0. Conversion from denary to binary allows us to convert decimal numbers to bits that computers can use.

  • Write down the decimal number.

  • Divide it by 2 and take note of the remainder. For example, you want to convert 1511 to binary. Divide 1511 by 2. The result is 755 with remainder 1.

  • Divide the resulting whole number by 2 again and take note of the remainder. In the example, 755 divided by 2 equals 377 with remainder 1.

  • Continue dividing the resulting whole number by 2 until the last remaining whole number is 1. Always take note of the remainder.

    In our example, dividing 377 results to 188 remainder 1.

    Further dividing 188 by 2 results to 94 remainder 0.

    94 divided by 2 is 47 remainder 0.

    47 divided by 2 is 23 remainder 1.

    23 divided by 2 is 11 remainder 1.

    11 divided by 2 is 5 remainder 1.

    5 divided by 2 is 2 remainder 1.

    2 divided by 2 is 1 remainder 0.

  • Write down the last two results of your continuous division. In the example, it is 2 divided by 2, which results to 1 remainder 0. This becomes the first two bits of the binary number: 1 and 0.

  • Write the remainders successively, working your way up until the very first division you've made. In our example, it was 1511 divided by 2, which is 755 remainder 1. The remainders that followed your last two division going up are: 111100111. Thus, 1511 in binary is 10111100111.

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