Welcome to our community

Be a part of something great, join today!

Determine the decimal values of the following unsigned numbers

shamieh

Active member
Sep 13, 2013
539
Determine the decimal value of the following unsigned number.

So here was the first one I did. Which is easy. I completely understand this one.

(3751)8 = 2025
I know this because: \(\displaystyle 1 + 5 * 8^1 + 7 * 8^2 + 3 * 8^3 = 2025.\)

But then they gave me this one.

b) (A25F)16. <-- They want me to determine the decimal value of the following unsigned number just as I did above, but I don't understand how they are getting their solution. Here is the solution they got..As you can see they did not write out all the steps so this is why I am confused. I want to know what's actually going on here. If anyone can clarify please help!

(A25F)16 = \(\displaystyle 15 * 1+ 5 *16 + 2 * 162+ 10 * 163 = 41567\)

Where does the 15 come from? What is the power they are multiplying by? (Wait)

Here is another solution I found, if this helps.

(A25F)16 = \(\displaystyle 10 * 4096 + 2 * 256 + 5 * 16 + 15 = 41567\)
 
Last edited:

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
They should have written:

\(\displaystyle (\text{A25F})_{16}=15 \cdot16^0+5 \cdot16^1+2 \cdot16^2+10 \cdot16^3=41567\)

In base 16 (or hexadecimal) notation, the letters A-F represent the decimal values of 10-15 respectively. Those letters are chosen as the 6 extra characters used to represent all of the needed digits.
 

shamieh

Active member
Sep 13, 2013
539
Awesome! Thanks Mark. I was staring at my screen for almost 30 minutes trying to figure out what was going on. :D