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taurus
1 month ago
5

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

Computers and Technology
1 answer:
Natasha_Volkova [897]1 month ago
7 0

Answer:

The decimal representation of 101₂² from base 2 equals 25 in base 10.

Explanation:

To derive the decimal equivalent of 101₂²;

101₂ × 101₂ results in 101₂ + 0₂ + 10100₂.

In this expression, we observe that the '2' in the hundred's place must be converted to '0' while carrying over '1' to the thousand's position, leading to;

101₂ + 0₂ + 10100₂ = 11001₂.

This shows that;

101₂² =  11001₂.

Next, we convert the outcome of squaring the base 2 number, 11001₂, into base 10 through the following method;

Converting 11001₂ to base 10 results in;

1 × 2⁴ + 1 × 2³ + 0 × 2² + 0 × 2¹ + 1 × 2⁰.

The calculation yields;

16 + 8 + 0 + 0 + 1 = 25₁₀.

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