Convert the binary number 00001111 to a decimal number.
Understand the Problem
The question is asking us to convert a binary number, specifically 00001111, into its decimal equivalent. To do this, we will interpret each digit of the binary number based on its position and calculate the corresponding decimal value.
Answer
The decimal equivalent of the binary number 00001111 is $15$.
Answer for screen readers
The decimal equivalent of the binary number 00001111 is 15.
Steps to Solve
- Identify the position values Each digit in a binary number represents a power of 2, starting from the rightmost digit at position 0. For the binary number 00001111, the positions and their corresponding powers of 2 are:
- 0: $2^0 = 1$
- 1: $2^1 = 2$
- 2: $2^2 = 4$
- 3: $2^3 = 8$
- 4: $2^4 = 16$
- 5: $2^5 = 32$
- 6: $2^6 = 64$
- 7: $2^7 = 128$
- Assign the binary digits to their position values Now, we will match each binary digit (0 or 1) to the appropriate power of 2. For 00001111:
- The digits from left to right are: 0, 0, 0, 0, 1, 1, 1, 1
- Their corresponding values are:
- $0 \cdot 2^7 = 0$
- $0 \cdot 2^6 = 0$
- $0 \cdot 2^5 = 0$
- $0 \cdot 2^4 = 0$
- $1 \cdot 2^3 = 8$
- $1 \cdot 2^2 = 4$
- $1 \cdot 2^1 = 2$
- $1 \cdot 2^0 = 1$
- Calculate the decimal value Add the values of the binary digits that are '1': $$ 0 + 0 + 0 + 0 + 8 + 4 + 2 + 1 = 15 $$
The decimal equivalent of the binary number 00001111 is 15.
More Information
The binary number system is base-2, where each digit represents a power of 2. In this case, the binary number 00001111 corresponds to the decimal number 15, which can be verified by summing up the values of the positions where there are '1's.
Tips
- Miscounting the positions: Always start from the rightmost digit (position 0).
- Forgetting to multiply by the power of 2: Ensure each '1' is multiplied by its corresponding power of 2 before adding.
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