Question

Which decimal value (base 10) is equal to the binary number 1012?

Answer 1

Answer:

The decimal value of 101₂² base 2 = 25 base 10

Explanation:

The number 101₂² in decimal value is found as follows;

101₂ × 101₂ = 101₂ + 0₂ + 10100₂

We note that in 101 + 10100 the resultant 2 in the hundred position will have to be converted to a zero while carrying over 1 to the thousand position to give;

101₂ + 0₂ + 10100₂ = 11001₂

Therefore;

101₂² =  11001₂

We now convert the result of the square of the base 2 number, 101², which is 11001₂ to base 10 as follows;

Therefore converting 11001₂ to base 10 gives;

11001₂= 1 × 2⁴ + 1 × 2³ + 0 × 2² + 0 × 2 ¹ + 1 × 2⁰

Which gives;

16 + 8 + 0 + 0 + 1 = 25₁₀.