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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.
