Convert 101101 to decimal.

Understand the Problem

The question is asking to convert a binary number (101101) into its decimal representation. This involves calculating the sum of each digit multiplied by 2 raised to the power of its position from the right, starting at 0.

Answer

The decimal representation of the binary number 101101 is 45.

Steps to Solve

Identify the binary digits and positions

Write down the binary number and determine the position of each digit from right to left. For the binary number 101101, we have:

Position 0: 1
Position 1: 0
Position 2: 1
Position 3: 1
Position 4: 0
Position 5: 1

Calculate the decimal value for each digit

Each binary digit is multiplied by $2$ raised to the power of its position. The contributions from each digit in 101101 can be calculated as follows:

For position 0: $1 \times 2^0 = 1$
For position 1: $0 \times 2^1 = 0$
For position 2: $1 \times 2^2 = 4$
For position 3: $1 \times 2^3 = 8$
For position 4: $0 \times 2^4 = 0$
For position 5: $1 \times 2^5 = 32$

Sum all the contributions

Now, add up all the values obtained from step 2: $$ 1 + 0 + 4 + 8 + 0 + 32 = 45 $$

The decimal representation of the binary number 101101 is 45.

More Information

The process of converting binary to decimal is fundamental in computer science, as computers operate using binary. Each binary digit (bit) represents an increasing power of 2, allowing us to calculate the decimal equivalent easily.

Tips

Forgetting to multiply by $2$ raised to the correct position. Always ensure you start counting positions from the right, beginning at 0.
Miscalculating the contributions of the digits, especially if they are either 0 or 1, and not summing them correctly.

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