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!