Question

What is the unsigned decimal representation of each hexadecimal integer?

Answer 1

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 $16^{1}$ + 10 x $16^{0}$

=> 3A = 48 + 10

=> 3A = 58 (in decimal)

(b) 1BF = 1 x $16^{2}$ + 11 x $16^{1}$ + 15 x $16^{0}$

=> 1BF = 256 + 176 + 15

=> 1BF = 447 (in decimal)

(c) 4096 = 4 x $16^{3}$ + 0 x $16^{2}$ + 9 x $16^{1}$ + 6 x $16^{0}$

=> 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,

$4^{0}$ = 1

$59^{0}$ = 1