Question

What is the unsigned decimal representation of each hexadecimal integer?

a. 3A
b. 1BF
c. 4096

Answer 1

(a) 58

(b) 447

(c) 16534

Step-by-step 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