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Understanding hexadecimal (base-16) notation and it’s relevance to decimal numbers might be very handy, especially when dealing with computer systems and digital electronics. Let’s start with the hexadecimal number 0xff. In decimal (base-10), 0xff can be converted by breaking it down into its individual digits. The ‘f’ in hexadecimal represents the decimal value of 15. Therefore, 0xff can be expressed as:

0xff = (15 × 16^1) + (15 × 16^0)

This calculation gives us:

0xff = (15 × 16) + (15 × 1) = 240 + 15 = 255

Thus, 0xff in decimal is 255.

Now, let’s extend our understanding to other hexadecimal values. Take 0xffff for instance. Following the same method, we see that 0xffff consists of four ‘f’ characters. This can be calculated as:

0xffff = (15 × 16^3) + (15 × 16^2) + (15 × 16^1) + (15 × 16^0)

Performing the calculations gives us:

0xffff = (15 × 4096) + (15 × 256) + (15 × 16) + (15 × 1)

Which simplifies to:

0xffff = 61440 + 3840 + 240 + 15 = 65535

Therefore, 0xffff in decimal is 65535.

Lastly, consider 0xffffff, which is represented by six ‘f’ characters. The conversion works similarly:

0xffffff = (15 × 16^5) + (15 × 16^4) + (15 × 16^3) + (15 × 16^2) + (15 × 16^1) + (15 × 16^0)

Breaking it down:

0xffffff = (15 × 1048576) + (15 × 65536) + (15 × 4096) + (15 × 256) + (15 × 16) + (15 × 1)

Which totals to:

0xffffff = 15728640 + 983040 + 61440 + 3840 + 240 + 15 = 16777215

Thus, 0xffffff in decimal is 16777215.

In summary, converting hexadecimal to decimal involves multiplying each digit by 16 raised to the power of its position (starting from 0 on the right). This process applies to any hexadecimal number, and with practice, you’ll find it becomes second nature. Keep honing your skills, and soon you’ll be a pro at these conversions!