Convert 1011 binary to decimal
Understand the Problem
The question is asking for the conversion of a binary number (1011) into its decimal equivalent. The binary system is base-2, and the decimal system is base-10. We will evaluate each bit of the binary number by calculating its value based on its position.
Answer
11
Answer for screen readers
The final answer is 11
Steps to Solve
- Identify the positions of the bits
Each bit in a binary number represents a power of 2, starting from the rightmost bit (which is position 0). For the binary number 1011, the bit positions are as follows: 1 (position 3), 0 (position 2), 1 (position 1), and 1 (position 0).
- Calculate the decimal value of each bit
Multiply each bit by $2^{ ext{position}}$ to find its decimal value. $$ 1 imes 2^3 = 8 $$ $$ 0 imes 2^2 = 0 $$ $$ 1 imes 2^1 = 2 $$ $$ 1 imes 2^0 = 1 $$
- Sum the decimal values
Add the decimal values of each bit obtained in the previous step: $$ 8 + 0 + 2 + 1 = 11 $$
The final sum is the decimal equivalent of the binary number 1011.
The final answer is 11
More Information
Binary numbers are fundamental in digital electronics and computing because they are the simplest number system in which information can be represented and processed.
Tips
A common mistake is forgetting that the rightmost bit is the least significant bit (LSB) and represents $2^0$. Make sure to correctly assign the power of 2 to each bit based on its position.
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