Math Problem Statement
Add in base two: 111_2 + 11_2
Solution
To solve the binary addition of , we'll follow the rules of binary addition, which are:
- (which is 0 with a carry of 1)
- (which is 1 with a carry of 1)
Let's add these binary numbers step-by-step:
& 1 & 1 & 1 \\ + & 0 & 1 & 1 \\ \hline & 1 & 0 & 1 & 0 \\ \end{array}$$ **Step-by-Step Addition:** 1. **Rightmost Column:** $$1 + 1 = 10$$ (write down 0, carry 1) 2. **Middle Column:** $$1 + 1 + 0 = 10$$ (write down 0, carry 1) 3. **Leftmost Column:** $$1 + 1 = 10$$ (write down 1) So, the final result of $$111_2 + 11_2$$ in base two is: $$1010_2$$ ### Do you want more details or have any questions? Here are some related questions you might consider: 1. How would you perform subtraction in binary? 2. What is the decimal equivalent of the binary number $$1010_2$$? 3. How can you add three or more binary numbers together? 4. What are some real-world applications of binary arithmetic? 5. What are the rules for multiplying two binary numbers? **Tip:** When adding binary numbers, always remember to carry over to the next higher bit when the sum of a column exceeds 1.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Binary Arithmetic
Base Systems
Formulas
Binary Addition Rules
Theorems
Binary Carry Over
Suitable Grade Level
Grades 6-8