Answer:
(a) 58
(b) 447
(c) 16534
Explanation:
Since these integers are in hexadecimal format, it is worthy to know or note that;
A => 10
B => 11
C => 12
D => 13
E => 14
F => 15
Therefore, using these, let's convert the following to decimal:
(a) 3A = 3 x [tex]16^{1}[/tex] + 10 x [tex]16^{0}[/tex]
=> 3A = 48 + 10
=> 3A = 58 (in decimal)
(b) 1BF = 1 x [tex]16^{2}[/tex] + 11 x [tex]16^{1}[/tex] + 15 x [tex]16^{0}[/tex]
=> 1BF = 256 + 176 + 15
=> 1BF = 447 (in decimal)
(c) 4096 = 4 x [tex]16^{3}[/tex] + 0 x [tex]16^{2}[/tex] + 9 x [tex]16^{1}[/tex] + 6 x [tex]16^{0}[/tex]
=> 4096 = 4 x 4096 + 0 + 144 + 6
=> 4096 = 16534 (in decimal)
Note:
Do not forget that any number greater than zero, when raised to the power of zero gives 1.
For example,
[tex]4^{0}[/tex] = 1
[tex]59^{0}[/tex] = 1
