Convert binary 111 to decimal.
Understand the Problem
The question is asking to convert the binary number 111 into decimal format. This involves taking each digit of the binary number and calculating its decimal equivalent based on its position from right to left.
Answer
$7$
Answer for screen readers
The decimal equivalent of the binary number 111 is $7$.
Steps to Solve
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Identify Binary Digits and Their Positions The binary number is composed of the digits 1, 1, and 1. Each digit represents a power of 2 based on its position, starting from the right (0 for the rightmost digit).
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Calculate Each Digit's Decimal Value Each digit in the binary number will be multiplied by $2$ raised to the power of its position.
For the binary number 111:
- The rightmost digit (1) is at position 0: $1 \times 2^0 = 1 \times 1 = 1$
- The middle digit (1) is at position 1: $1 \times 2^1 = 1 \times 2 = 2$
- The leftmost digit (1) is at position 2: $1 \times 2^2 = 1 \times 4 = 4$
- Sum All Decimal Values Now, add the decimal values calculated from each position:
$$ 1 + 2 + 4 = 7 $$
Hence, the decimal equivalent of the binary number 111 is 7.
The decimal equivalent of the binary number 111 is $7$.
More Information
Converting binary to decimal is a common method used in computer science and digital electronics, as binary is the fundamental language of computers.
Tips
- A common mistake is forgetting to account for the power of 2 as you move left from the rightmost digit. Always remember that the rightmost digit is $2^0$, the next is $2^1$, and so forth.
- Sometimes people might miscalculate the sums. It helps to write each value down clearly to avoid confusion.
