Math Problem Statement

Complete the following binary arithmetic operations (Show your work): A. 101110 + 110011 B. 1011000 - 111111

Solution

Let's solve these binary operations step by step.


A. Binary Addition: 101110 + 110011

  1. Align the numbers:

        101110  
      + 110011
    
  2. Add column by column from right to left:

    • 0 + 1 = 1
    • 1 + 1 = 10 (write 0, carry 1)
    • 1 + 0 + 1 (carry) = 10 (write 0, carry 1)
    • 1 + 0 + 1 (carry) = 10 (write 0, carry 1)
    • 0 + 1 + 1 (carry) = 10 (write 0, carry 1)
    • 1 + 1 + 1 (carry) = 11 (write 1, carry 1)
  3. Write the final result:

    1100001
    

B. Binary Subtraction: 1011000 - 111111

  1. Convert to same number of digits by adding leading zeroes:

    1011000  
    - 0111111  
    
  2. Perform subtraction column by column:

    • 0 - 1 → borrow from the next available digit.
    • Subtract step by step using binary borrowing rules.
  3. Calculation result:

    0 1
    

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Math Problem Analysis

Mathematical Concepts

Binary Arithmetic
Addition
Subtraction

Formulas

Binary Addition Rules
Binary Subtraction with Borrowing

Theorems

None (Basic Arithmetic Operations)

Suitable Grade Level

Grades 7-9