Conversions Examples

In the first example the decimal integer 2012 is converted in binary by using the division method.

We proof here by realizing the sum of products of the digital bits from the obtained number with the corresponding weight (the power of 2 coresponding to its position).

In the following we proof the result by converting this in decimal using the division method. We divide the binary number to the value of the decimal number base 10 expressed in binary. The division uses the same rules as the one you use in conventional algebra when dividing decimal numbers.

In the following example the conversion is illustrated for the octal number system. The conversion steps are similar with those used for binary. As a remark, because the base is 3 times greather than the binary (is a power of that) the number of divisions reduces proportionally.

When a base involved in conversion is a power of the other one is possible to apply a direct conversion between the numbers. In the following examples is illustrated the direct conversion between binary (2) numbers and octal (8=2³) and hexadecimal (16=2⁴).

The following examples illustrates the conversion of real naumbers (numbers having an integral part and a fraction part) in octal and hexadecimal together with a direct conversion in binary.

Conversions to hexadecimal.