Convert 111111 to decimal.
Understand the Problem
The question is asking to convert the binary number 111111 into its decimal equivalent. This involves calculating the value of each digit in the binary system based on its position.
Answer
$63$
Answer for screen readers
The decimal equivalent of the binary number $111111$ is $63$.
Steps to Solve
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Identify the binary number The binary number given is $111111$. We know that each binary digit (bit) represents a power of 2, starting from the rightmost bit, which is $2^0$.
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Convert each bit to decimal We will convert each bit to its decimal equivalent by multiplying it by $2$ raised to the power of its position.
- From right to left:
- The 1st bit (from right): $1 \times 2^0 = 1 \times 1 = 1$
- The 2nd bit: $1 \times 2^1 = 1 \times 2 = 2$
- The 3rd bit: $1 \times 2^2 = 1 \times 4 = 4$
- The 4th bit: $1 \times 2^3 = 1 \times 8 = 8$
- The 5th bit: $1 \times 2^4 = 1 \times 16 = 16$
- The 6th bit: $1 \times 2^5 = 1 \times 32 = 32$
- Sum the decimal values Now we will sum all the decimal values we just calculated:
$$ 1 + 2 + 4 + 8 + 16 + 32 = 63 $$
- Final Result The decimal equivalent of the binary number $111111$ is therefore $63$.
The decimal equivalent of the binary number $111111$ is $63$.
More Information
Binary numbers are a base-2 numeral system, which means they only use two symbols: 0 and 1. Each binary digit represents a power of 2, making the conversion to decimal straightforward through positional multiplication.
Tips
- Misunderstanding the power of each bit's position can lead to incorrect calculations. Make sure to start counting from $0$ from the right.
- Forgetting to sum all the calculated decimal values results in an incomplete answer.
