Understanding 1's Complement
1's complement is a method for representing negative binary numbers. To find the 1's complement of a binary number, you simply invert all the bits: change 0s to 1s and 1s to 0s.
Given Number
The number provided is -011012. Here, the 'minus' sign indicates that we need to find the 1's complement of the positive binary equivalent of the number.
Identify the Binary Equivalent
- The number is given in binary as 01101.
- The first step is to identify the bits:
- 0 → 0
- 1 → 1
- 1 → 1
- 0 → 0
- 1 → 1
- Thus, 01101 is the binary representation of the number 13 in decimal.
Calculating 1's Complement
To find the 1's complement, we invert each bit of 01101:
- 0 → 1
- 1 → 0
- 1 → 0
- 0 → 1
- 1 → 0
Thus, the 1's complement of 01101 is 10010.
Final Representation
Since the original number was negative (-01101), its 1's complement is represented in the binary system as 10010.
Options Analysis
Now, let's examine the options provided:
- a) 01010
- b) 10011
- c) 10010
- d) 01011
From the analysis, the correct answer is option C: 10010.
This confirms that the 1's complement of -01101 is indeed 10010.