Convert 110 from binary to decimal.
Understand the Problem
The question is asking how to convert the binary number 110 into its decimal equivalent. This involves understanding the positional values of binary digits and calculating the sum based on those values.
Answer
The decimal equivalent of the binary number 110 is $6$.
Answer for screen readers
The decimal equivalent of the binary number 110 is 6.
Steps to Solve
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Identify the Binary Number The given binary number is 110. This number consists of three digits: 1, 1, and 0.
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Assign Positional Values From right to left, the positional values for the binary number are:
- The rightmost digit is at position $2^0 = 1$
- The next digit is at position $2^1 = 2$
- The leftmost digit is at position $2^2 = 4$
- Calculate the Decimal Value Now multiply each binary digit by its corresponding positional value:
- The leftmost digit (1) is at position $2^2$: $1 \times 4 = 4$
- The middle digit (1) at position $2^1$: $1 \times 2 = 2$
- The rightmost digit (0) at position $2^0$: $0 \times 1 = 0$
- Sum the Results Add the results of the calculations together: $$ 4 + 2 + 0 = 6 $$
The decimal equivalent of the binary number 110 is 6.
More Information
The conversion from binary to decimal involves understanding how binary numbers are structured based on powers of 2. Each digit contributes to the overall value based on its position.
Tips
- Miscalculating Powers of Two: Make sure to correctly calculate $2^0$, $2^1$, $2^2$, etc.
- Forgetting to Add Values: Remember to sum all the values after multiplying.
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