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
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Align the numbers:
101110 + 110011
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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)
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Write the final result:
1100001
B. Binary Subtraction: 1011000 - 111111
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Convert to same number of digits by adding leading zeroes:
1011000 - 0111111
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Perform subtraction column by column:
- 0 - 1 → borrow from the next available digit.
- Subtract step by step using binary borrowing rules.
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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
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