Determine the decimal values of the following unsigned numbers

[shamieh]

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 = \(\displaystyle 10 * 4096 + 2 * 256 + 5 * 16 + 15 = 41567\)

 

[MarkFL]

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]

Awesome! Thanks Mark. I was staring at my screen for almost 30 minutes trying to figure out what was going on. :D