What is 101 in binary?
Understand the Problem
The question is asking how to convert the decimal number 101 into its binary representation. This involves determining which powers of 2 add up to 101 and expressing it in binary format.
Answer
The binary representation of 101 is $1100101$.
Answer for screen readers
The binary representation of 101 is $1100101$.
Steps to Solve
- Identify the largest power of 2 less than 101
Start by identifying the powers of 2: $2^0 = 1$, $2^1 = 2$, $2^2 = 4$, $2^3 = 8$, $2^4 = 16$, $2^5 = 32$, $2^6 = 64$, and $2^7 = 128$. The largest power of 2 less than 101 is $2^6 = 64$.
- Subtract and repeat
Next, subtract 64 from 101: $$101 - 64 = 37$$ Now, find the largest power of 2 less than 37. The largest is $2^5 = 32$.
- Continue the process
Subtract again: $$37 - 32 = 5$$ Now, find the largest power of 2 less than 5, which is $2^2 = 4$. Subtract: $$5 - 4 = 1$$
- Identify the final power of 2
The final number is 1, which is $2^0$. Now, we have identified the powers of 2 used:
- $2^6 = 64$
- $2^5 = 32$
- $2^2 = 4$
- $2^0 = 1$
- Construct the binary representation
In binary, each power of 2 corresponds to a digit in the binary number (1 means the power is used, 0 means it is not). Therefore, the binary representation for 101 is:
- For $2^6$: 1
- For $2^5$: 1
- For $2^4$: 0 (not used)
- For $2^3$: 0 (not used)
- For $2^2$: 1
- For $2^1$: 0 (not used)
- For $2^0$: 1
Putting this together gives us binary: $1100101$.
The binary representation of 101 is $1100101$.
More Information
The binary representation system uses only two digits: 0 and 1. It is widely used in computer science and digital electronics because computers operate using binary logic.
Tips
- Forgetting to consider all powers of 2 less than the target number.
- Miscounting the positions while constructing the binary number.
- Confusing which powers were used and which were not, leading to incorrect binary digits.
