# Converting to decimal and hexadecimal

• Sep 1st 2008, 10:11 AM
Tom Pattiz
I am having trouble with a couple of problems. Here they are:

Convert 101100012 to decimal

Convert 2E16 to decimal

I can figure out the conversion, but am not sure what the sub notation means.

• Sep 1st 2008, 10:55 AM
Soroban
Hello, Tom!

I assume there is a typo in #3 . . .

Quote:

1) Convert $\displaystyle 10110001_2$ to decimal

2) Convert $\displaystyle 2E_{16}$ to decimal

3) Convert $\displaystyle {\color{red}1}01011111001_2$ to hexadecimal.

I can figure out the conversion,
but am not sure what the sub notation means. . . . . really?

The subscripts represent the bases.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

$\displaystyle 1)\;\;10110001_2$ is in base-2.

We have: .$\displaystyle 1\!\cdot\!2^7 + 0\!\cdot\!2^6 + 1\!\cdot\!2^5 + 1\!\cdot\!2^4 + 0\!\cdot\!2^3 + 0\!\cdot\!2^2 + 0\!\cdot\!2^1 + 1$

. . . . . . $\displaystyle = \;128 + 0 + 32 + 16 + 0 + 0 + 0 + 1 \;=\;177$

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

$\displaystyle 2)\;\;2E_{16}$ is in base-16.

We have: .$\displaystyle 2\!\cdot\!16^1 + 14\!\cdot\!1 \;=\;46$

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

$\displaystyle 3)\;\;1010 1111 1001_2$ is in base-2.

To write it in base-16:

. . $\displaystyle \text{we have: }\;\underbrace{1010}_{10} \underbrace{1111}_{15} \underbrace{1001}_{9}$
. . . . . . . . . .$\displaystyle \downarrow \quad\;\, \downarrow \quad\;\;\:\downarrow$
. . . . . . . $\displaystyle = \;\;A\quad\,F\quad\;\;\, 9$

. . . . . . . $\displaystyle = \;\;AF9_{16}$

• Sep 1st 2008, 11:03 AM
Tom Pattiz
THANK YOU.
Thanks for the quick response.