The 1's complement of binary number 10010 is
01101
Finding the 1's Complement of a Binary Number
Understanding how to find the 1's complement of a binary number is a fundamental concept in digital electronics and computer systems. The 1's complement is used in binary arithmetic, particularly for representing negative numbers and performing subtraction.
What is 1's Complement?
The 1's complement of a binary number is obtained by inverting each bit of the number. This means changing every 0 to a 1 and every 1 to a 0.
Step-by-Step Calculation
We are asked to find the 1's complement of the binary number $\text{10010}_{2}$. To do this, we will go through each bit of the number from left to right (or right to left, it doesn't matter for 1's complement) and flip it.
- Start with the binary number: $\text{10010}_{2}$.
- Look at the first bit (leftmost): It is 1. Change it to 0. The number starts becoming $\text{0...}$
- Look at the second bit: It is 0. Change it to 1. The number becomes $\text{01...}$
- Look at the third bit: It is 0. Change it to 1. The number becomes $\text{011...}$
- Look at the fourth bit: It is 1. Change it to 0. The number becomes $\text{0110...}$
- Look at the fifth bit (rightmost): It is 0. Change it to 1. The number becomes $\text{01101}$.
Thus, the 1's complement of $\text{10010}_{2}$ is $\text{01101}_{2}$.
Summary Table
| Original Binary Number ($\text{10010}_{2}$) | Bit Inversion | 1's Complement ($\text{01101}_{2}$) |
|---|---|---|
| 1 | $\rightarrow$ | 0 |
| 0 | $\rightarrow$ | 1 |
| 0 | $\rightarrow$ | 1 |
| 1 | $\rightarrow$ | 0 |
| 0 | $\rightarrow$ | 1 |
Conclusion
By inverting each bit of the binary number $\text{10010}_{2}$, we get $\text{01101}_{2}$. Comparing this result with the given options, we find that it matches option 1.
Revision Table: Binary Complements
| Concept | Description | How to Calculate |
|---|---|---|
| 1's Complement | Inverting all bits (0 becomes 1, 1 becomes 0). | Flip each bit of the binary number. |
| 2's Complement | Used widely for signed binary arithmetic. | Find the 1's complement and then add 1 to the least significant bit (rightmost bit). |
Additional Information: Why Use Complements?
Binary complements, especially 2's complement, are crucial in digital systems for several reasons:
- Signed Number Representation: They allow representation of both positive and negative binary numbers in a way that makes arithmetic operations easier.
- Subtraction as Addition: Using 2's complement, subtraction can be performed by adding the complement of the subtrahend, simplifying the design of arithmetic logic units (ALUs) in processors.
- Arithmetic Operations: Complements simplify the logic required to perform addition and subtraction within computer hardware.
The 1's complement is often an intermediate step towards finding the 2's complement or is used in certain specific algorithms.
Important Questions from Number Representation
Which of the following pairs of octal and binary numbers are NOT equal?
The greatest negative number which can be stored in a 8-bit register using 2's complement arithmetic is
Which of the following codes is also known as reflected binary code?
What is the octal equivalent of (F3B1)16?
Convert the hexadecimal number C6 to binary number.
