# How does the number of digits change as the number is progressively converted from binary to octal to decimal to hexadecimal system?

Apr 2, 2017

Number of digits used to represent any number continuously decreases.

#### Explanation:

As the number is progressively converted from binary to octal to decimal to hex, the number of digits used to represent any number continuously decreases.

For example

${\left(100101010111100110111101111\right)}_{2}$ - Binary - twenty seven digits

= ${\left(452746757\right)}_{8}$ - Octal - nine digits

= ${\left(78368239\right)}_{10}$ - Decimal - eight digits

= ${\left(4 A B C D E F\right)}_{16}$ - Hexagesimal - seven digits.

Note that decline in number of digits, from Decimal to Octal is not much as difference between bases is not much and in some cases it may be equal. For example

${\left(52746757\right)}_{8} = {\left(11259375\right)}_{10} = {\left(A B C D E F\right)}_{16}$.

But this will never increase.