Math Problem Statement

Add binary number 10110 to binary number 111001

Solution

To add the binary numbers 1011010110 and 111001111001, follow these steps:

  1. Align the numbers by their least significant bit (rightmost digit), padding the smaller number with zeros at the beginning: 00010110(binary for 22)00010110 \quad \text{(binary for 22)} 111001(binary for 57)111001 \quad \text{(binary for 57)}

  2. Perform binary addition, remembering the rules:

    • 0+0=00 + 0 = 0
    • 0+1=10 + 1 = 1
    • 1+1=101 + 1 = 10 (write 00, carry 11)
    • 1+1+1=111 + 1 + 1 = 11 (write 11, carry 11)

    Adding step by step:

      Carry:   1  1  1  0  0
      Numbers: 0  0  0  1  0  1  1  0
               + 1  1  1  0  0  1
      Result:  1  0  0  0  0  1  1
    
  3. The result is 10000111000011 in binary.

Final Answer:

The sum of 1011010110 and 111001111001 in binary is 10000111000011, which equals 6767 in decimal.

Would you like more details or further assistance? Here are some related questions to explore:

  1. How do you subtract binary numbers?
  2. Can you explain binary multiplication?
  3. How is binary addition applied in computer science?
  4. What is the difference between binary and hexadecimal addition?
  5. How do you convert binary to decimal manually?

Tip: When adding binary numbers, align them carefully and work from the rightmost bit to avoid errors with carries.

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Math Problem Analysis

Mathematical Concepts

Binary Addition
Number Systems

Formulas

Binary addition rules: 0 + 0 = 0, 0 + 1 = 1, 1 + 1 = 10 (write 0, carry 1), 1 + 1 + 1 = 11 (write 1, carry 1)

Theorems

Place Value System in Binary

Suitable Grade Level

Grades 6-8