Correct Answer - Option 2 : 45816
Concept:-
Hexadecimal number system: Hexadecimal is a radix-16 or base-16 number system, while in our day-to-day life in computers and digital logic we use a base-2 (binary) number system, but it is visually more efficient to use base-16 (Hexadecimal) number system.
Decimal number system: The most common base-10 number system that we use frequently.
Decimal
|
Hexadecimal
|
Decimal
|
Hexadecimal
|
0
|
0
|
8
|
8
|
1
|
1
|
9
|
9
|
2
|
2
|
10
|
A
|
3
|
3
|
11
|
B
|
4
|
4
|
12
|
C
|
5
|
5
|
13
|
D
|
6
|
6
|
14
|
E
|
7
|
7
|
15
|
F
|
In general
(an × rn) +… (a1 × r1) + (a0 × r0) + (a-1 × r-1) +…….. (a-m × r-m) -------(1)
Where an = Hexadecimal number at the nth place.
The above expansion of a number in any radix r, always gives back the decimal equivalent of the number.
Calculation:-
Given,
Hexadecimal number is (B2F8)16
Expanding according to equation 1,
(B × 163) + (2 × 162) + (F × 161) + (8 × 160)
= (11 × 4096) + (2 × 256) + (15 × 16) + (8)
= (45816)10
So, the decimal equivalent of the given hexadecimal number is (45816)10.