What is 7 as a 4-bit binary number?
Understand the Problem
The question is asking how to represent the decimal number 7 in a 4-bit binary format. This involves converting the decimal number to binary, ensuring that the result is exactly 4 bits long.
Answer
The 4-bit binary representation of the decimal number 7 is $0111$.
Answer for screen readers
The 4-bit binary representation of the decimal number 7 is $0111$.
Steps to Solve
- Convert the decimal number to binary To convert the decimal number 7 to binary, we need to divide the number by 2 and keep track of the remainders.
- 7 divided by 2 equals 3 with a remainder of 1.
- 3 divided by 2 equals 1 with a remainder of 1.
- 1 divided by 2 equals 0 with a remainder of 1.
Writing the remainders from bottom to top gives us the binary number: 111.
- Ensure the result is 4 bits long Since the binary representation of 7 is 111, which is only 3 bits long, we need to add a leading zero to make it 4 bits long.
Thus, we prepend a 0 to the binary number:
$$ 0111 $$
- Final representation The final 4-bit binary representation of the decimal number 7 is thus:
$$ 0111 $$
The 4-bit binary representation of the decimal number 7 is $0111$.
More Information
In binary, each bit represents a power of 2. The 4-bit system can represent numbers from 0 ($0000$) to 15 ($1111$), giving it the capacity to cover the range required for this conversion.
Tips
- Forgetting to add a leading zero to make sure the binary number is 4 bits long. Always check the total number of bits after converting.
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