Convert 0110 to decimal.
Understand the Problem
The question is asking for the conversion of the binary number 0110 into its decimal equivalent. This requires converting the binary base (base 2) into decimal base (base 10) by calculating the values of the binary digits.
Answer
$6$
Answer for screen readers
The decimal equivalent of the binary number 0110 is $6$.
Steps to Solve
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Identify the binary number The binary number given is 0110.
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Assign powers of 2 to each digit From right to left, assign powers of 2 starting from 0:
- The 0 on the far right is $2^0$
- The next 1 is $2^1$
- The next 1 is $2^2$
- The 0 on the far left is $2^3$
This gives us the following representation:
- $0 \cdot 2^3$, $1 \cdot 2^2$, $1 \cdot 2^1$, $0 \cdot 2^0$
- Calculate the decimal values Now compute the contribution of each binary digit:
- $0 \cdot 2^3 = 0$
- $1 \cdot 2^2 = 4$
- $1 \cdot 2^1 = 2$
- $0 \cdot 2^0 = 0$
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Sum the decimal values Add together all the decimal values calculated: $$ 0 + 4 + 2 + 0 = 6 $$
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Write the final decimal equivalent The decimal equivalent of the binary number 0110 is 6.
The decimal equivalent of the binary number 0110 is $6$.
More Information
In binary, each digit represents a power of 2, and the leftmost digit is the most significant. Binary is the basis of digital electronics and computing.
Tips
- Forgetting to assign powers of 2 correctly: Ensure you're starting from $2^0$ on the far right and increasing to the left.
- Not converting the binary digits properly: Remember that a binary digit of '0' contributes nothing, while '1' contributes its power of 2.
