Math Problem Statement
what is the 2 s complement of 101011
Solution
To find the 2's complement of a binary number, follow these steps:
Step 1: Invert the bits (1's complement)
Invert each bit of the binary number. This means:
- Replace all 1's with 0's
- Replace all 0's with 1's
For the binary number 101011, the 1's complement is:
010100
Step 2: Add 1 to the result
Now, add 1 to the 1's complement:
010100
+ 1
--------
010101
So, the 2's complement of 101011 is 010101.
Would you like further details on 2's complement, or do you have another question?
Here are some related questions:
- How do you convert a negative decimal number to its 2's complement form?
- What are the differences between 1's complement and 2's complement?
- How do you convert a 2's complement binary number back to its original form?
- Can 2's complement be used to represent both positive and negative numbers in binary?
- How would you find the 2's complement of a larger binary number, such as 1101101?
Tip: To check your 2's complement, you can always convert it back to decimal and verify that it corresponds to the negation of the original number.
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Math Problem Analysis
Mathematical Concepts
Binary Arithmetic
Two's Complement
Number Systems
Formulas
1's complement: Invert each bit of the binary number
2's complement: Add 1 to the 1's complement
Theorems
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Suitable Grade Level
Grades 9-12
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