What is the decimal equivalent of the binary number 101101?
45
To convert a binary number to a decimal number, you need to understand the positional value of each bit in the binary sequence. Each bit represents a power of 2, starting from 0 on the far right. We will convert the binary number \(101101_2\) into its decimal form following these steps:
- Write down the positions of each bit from right to left, starting with 0. For \(101101_2\), this would be:
\(2^5,\ 2^4,\ 2^3,\ 2^2,\ 2^1,\ 2^0\) - Match each bit in the binary number with its positional value:
- The first bit (from left) is 1, which corresponds to \(2^5\).
- The second bit is 0, corresponding to \(2^4\).
- The third bit is 1, corresponding to \(2^3\).
- The fourth bit is 1, corresponding to \(2^2\).
- The fifth bit is 0, corresponding to \(2^1\).
- The sixth bit is 1, corresponding to \(2^0\).
- Calculate the decimal value represented by each positional bit being set to 1:
- \(1 \times 2^5 = 32\)
- \(0 \times 2^4 = 0\)
- \(1 \times 2^3 = 8\)
- \(1 \times 2^2 = 4\)
- \(0 \times 2^1 = 0\)
- \(1 \times 2^0 = 1\)
- Add up all the values obtained in the third step:
- \(32 + 0 + 8 + 4 + 0 + 1 = 45\)
Therefore, the decimal equivalent of the binary number \(101101_2\) is 45.
The correct answer is therefore 45, confirming it as the correct option from the given choices.
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