# (B2F8)16 = (?)10 What should come in the place of question mark?

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(B2F8)16 = (?)10
What should come in the place of question mark?
1. 51246
2. 45816
3. 32678
4. 10240

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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
(a× rn) +… (a× r1) + (a× 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.