Question

Convert the following hexadecimal numbers to decimal: (a) FF (b) F0A2 (c) 0F100 (d) 100

Answer 1

a) 255

b) 61602

c)

d)

Step-by-step explanation:

You need to understand the decimal equivalent of hexadecimal numbers, from 0 to 9 numbers are represented the same way, from 10 to 15 we use the alphabet, meaning 10 equals A in hexadecimal base, 11-B, 12-C, 13-D, 14-E, and 15-F.

For your first exercise you'll enumerate the number's positions fromright to lef begining with 0:

a. F F

position 1 0

Now you'll multiply your hexadecimal number (using the decimal equivalent for your letters) for the base (16) elevated to the number of the position:

`F*16^(0)=15*1=15\\F*16^(1)=15*16=240`

Finally, you'll add your results:

240+15=255

FF=255

b. F 0 A 2

position 3 2 1 0

`2*16^(0)=2*1=2\\A*16^(1)=10*16=160\\0*16^(2)=0*256=0\\F*16^(3)=16*4096=61440\\\\2+160+0+61440=61602\\`

F0A2=61602

c. F 1 0 0

position 3 2 1 0

`0*16^(0)=0*1=0\\0*16^(1)=0*16=0\\1*16^(2)=1*256=256\\F*16^(3)=16*4096=61440\\0+0+256+61440=61696\\`

0F100=61696

d. 1 0 0

position 2 1 0

`0*16^(0)=0*1=0\\0*16^(1)=0*16=0\\1*16^(2)=1*256=256\\\\0+0+256=256\\`

100=256

I hope you find this information useful! Good luck!