MHB Determine the decimal values of the following unsigned numbers

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The discussion focuses on converting unsigned numbers from octal and hexadecimal to decimal values. The user successfully converted (3751)8 to 2025 using the formula for base 8. However, confusion arises with converting (A25F)16 to decimal, particularly regarding the representation of the letter 'A' as 10 and the calculation steps. The correct conversion involves understanding that in hexadecimal, A-F represent decimal values 10-15, leading to the final decimal value of 41567. Clarification on the powers of 16 used in the conversion process helped resolve the user's confusion.
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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: $$1 + 5 * 8^1 + 7 * 8^2 + 3 * 8^3 = 2025.$$

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 = $$15 * 1+ 5 *16 + 2 * 162+ 10 * 163 = 41567$$

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 = $$10 * 4096 + 2 * 256 + 5 * 16 + 15 = 41567$$
 
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They should have written:

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

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