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:

  1. How do you convert a negative decimal number to its 2's complement form?
  2. What are the differences between 1's complement and 2's complement?
  3. How do you convert a 2's complement binary number back to its original form?
  4. Can 2's complement be used to represent both positive and negative numbers in binary?
  5. 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