University Maths question

Can anyone help me out with this badboy?

Find a method for converting a repeating expansion (with any period

t and any numbers of non-repeating digits between the point and the rst repeating digit) from binary tohexadecimal, without converting to base ten at any stage. Then convert the repeating binaryexpansion

10101.001101 (the last 5 digits 01101 are repeating)

to hexadecimal (without using base ten). [Note the one non-repeating digit before the re-

peating part.]

Re: University Maths question

Hello, lucasterry!

Quote:

Find a method for converting a repeating decimal expansion (with any period and any number of non-repeating digits

between the decimal point and the 1st repeating digit) from binary to hexadecimal, without converting to base ten.

Then convert the repeating binary expansion $\displaystyle 10101.0\overline{01101}$ to hexadecimal (without using base ten).

To convert $\displaystyle 11101001011100.011_2$ to hexadecimal, group the digits is sets of four,

. . starting at the decimal point and reading to the left and right.

We have: .$\displaystyle 11|1010|0101|1100|.0110| $

Convert each group to hexadecimal: .$\displaystyle \underbrace{11}_3|\underbrace{1010}_{10}| \underbrace{0101}_5|\underbrace{1100}_{12}|. \underbrace{0101}_6|$

Therefore: .$\displaystyle 3A5C.6_{16}$

We are given: .$\displaystyle 10101.0\overline{01101}_2$

We have: .$\displaystyle \underbrace{1}_1|\underbrace{0101}_5|.\underbrace{ 0011}_3|\underbrace{0101}_5|\underbrace{1010}_{10} |\underbrace{1101}_{13}|\underbrace{0110}_6| \underbrace{1011}_{11}|\underbrace{0101}_5| \underbrace{1010}_{10}|\underbrace{1101}_{13}| \hdots $

Therefore: .$\displaystyle 15.3\,\overline{5AD6B}_{16}$