Question

(10101) 2 = ( ? ) 10

Answer 1

$\huge\bigstar\:$$\Huge\tt\underline\blue{ANSWER}$

(10101)_2=(21)10

$\huge\bigstar\:$$\Huge\tt\underline\red{EXPLAINATION}$

Given : Number  (10101)_2(10101)2

To find : What is the value of  (10101)_2(10101)2 in decimal number system?

Solution :

Decimal number system is a positional numeral system employing 10 as the base.

Now, to convert it into base 10

Multiply each digit of the following binary by the corresponding power of 2:

(10101)_2(10101)2

=1\times 2^4+0\times 2^3+1\times 2^2+0\times 2^1+1\times 2^0=1×24+0×23+1×22+0×21+1×20

=1\times 16+0\times 8+1\times 4+0\times 2+1\times 1=1×16+0×8+1×4+0×2+1×1

=16+0+4+0+1=16+0+4+0+1

=21=21

Therefore,  (10101)_2=(21)_{10}(10101)2=(21)10