Question

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

Answer 1

Answer:

a) 255

b) 61602

c)

d)

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!