There are different number systems in mathematics. The most common is the decimal number system, which has 10 digits from 0 to 9. Other number systems include binary, octal and hexadecimal. The binary system uses only two digits, 0 and 1, and is used internal by computers. Octal has eight digits, from 0 to 7. Hexadecimal uses 16 (from 0 to 9, then A to F). The number systems can be converted from one to another using different conversion methods. Decimal to binary conversion involves continuous division, wherein a decimal number, like 256, is continuously divided by 2 with the remainder initially set aside, until the quotient reaches 1.
Step 1
Write down 256.
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Step 2
Divide 256 by 2 and take note of the remainder. This results to 128 remainder 0.
Step 3
Continue dividing the whole number result by 2 until the last whole number is 1. Always take note of the remainder. When you are finished, you should see this:
256 divided by 2 is equal to 128 remainder 0 128 divided by 2 is equal to 64 remainder 0 64 divided by 2 is equal to 32 remainder 0 32 divided by 2 is equal to 16 remainder 0 16 divided by 2 is equal to 8 remainder 0 8 divided by 2 is equal to 4 remainder 0 4 divided by 2 is equal to 2 remainder 0 2 divided by 2 is equal to 1 remainder 0.
Step 4
Write down the last result of the continuous division, which is 1, and then work your way up for the remainders of the continuous divisions. This results to 100000000, because all the remainders in this example are 0. Thus, 256 in binary is 100000000.