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Convert hex number to decimal.

(0101)16


1. 572
2. 527
3. 257
4. 253

1 Answer

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Best answer
Correct Answer - Option 3 : 257

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

Hexa-decimal

Decimal

Hexa-decimal

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 (0101)16              

Expanding according to equation 1,

(0 × 163) + (1 × 162) + (0 × 161) + (1 × 160)

= (0 × 4096) + (1 × 256) + (0 × 16) + (1 × 1)

= (257)10

So, the decimal equivalent of the given hexadecimal number is (257)10

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