I know that if we want to convert from base 16 to base 10 we do as follows (for example):

Given : $15C$ in base $16$

Conversion to base 10: $12 \times 16^0 + 5 \times 16^1 + 1 \times 16^2 = 348$ in base $10$

But I am unable to convert $15C.38$(base $16$) to base $10$.

You are watching: How to convert from base 10 to base 16

Can someone show how ?


After the "radix" point (the dot), we can just divide each integer in place $i$ counting from the left by $16^{i}$. So $0.36_{16} = 3/16+6/16^2$. This generalizes to all bases.


After the point, it goes like $16^{-1}$, $16^{-2}$ etc.

Therefore, $(15C.38)_{16}$ can be converted by doing the following:

$1 \times 16^2 + 5 \times 16^1 + 12 \times 16^0 + 3 \times 16^{-1} + 8 \times 16^{-2}$.

Another method is, writing every digit as 4-bit binary string and than converting those to decimal. i.e.

$(0001$ $0101$ $1100$ . $0011$ $1000)_{2} = (?)_{10}$


We have $15C_{16}=348_{10}$.

The fractional part is $0.38_{16}$ which is $(3\times 16^{-1})+(8\times 16^{-2})=0.21875$.

So $15C.38_{16}=348.21875_{10}$.


Thanks for contributing an answer to invernessgangshow.netematics Stack Exchange!

Please be sure to answer the question. Provide details and share your research!

But avoid

Asking for help, clarification, or responding to other answers.Making statements based on opinion; back them up with references or personal experience.

Use invernessgangshow.netJax to format equations. invernessgangshow.netJax reference.

See more: If Assets Are $300,000 And Liabilities Are $192,000, Then Equity Equals:

To learn more, see our tips on writing great answers.

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged computer-science binary or ask your own question.


site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. rev2021.10.18.40487

Your privacy

By clicking “Accept all cookies”, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy.