Binary to Decimal Conversion of 10101

Converting a binary number (base 2) to a decimal number (base 10) involves multiplying each binary digit by the corresponding power of 2 and summing the results. The position of each digit, starting from the rightmost digit as position 0, determines the power of 2.

Let's take the binary number 10101.

We identify the digits and their positions:

• The rightmost digit '1' is at position 0 (\(2^0\)).
• The next digit '0' is at position 1 (\(2^1\)).
• The next digit '1' is at position 2 (\(2^2\)).
• The next digit '0' is at position 3 (\(2^3\)).
• The leftmost digit '1' is at position 4 (\(2^4\)).

Now, we multiply each digit by the value of its position's power of 2:

To find the decimal equivalent of the binary number 10101, we sum the results from the last column:

\(16 + 0 + 4 + 0 + 1 = 21\)

So, the binary number 10101 is equivalent to the decimal number 21.