Math Problem Statement
10001+11011 in binary
Solution
To add the binary numbers and , let's perform the addition step by step:
\ \ 10001_2 \\ + 11011_2 \\ \hline \end{array}$$ ### Step 1: Add the rightmost bits (ones place): 1 + 1 = 10 (which means write down 0 and carry over 1). ### Step 2: Move to the next bit: 0 + 1 + 1 (carry) = 10 (write down 0 and carry over 1). ### Step 3: Move to the next bit: 0 + 0 + 1 (carry) = 1 (write down 1, no carry). ### Step 4: Move to the next bit: 1 + 1 = 10 (write down 0 and carry over 1). ### Step 5: Move to the leftmost bit: 1 + 1 + 1 (carry) = 11 (write down 1 and carry over 1). ### Step 6: After adding all the bits, we have a final carry of 1 to add in the leftmost place. The final result is: $$\begin{array}{c} 10001_2 \\ + 11011_2 \\ \hline 101100_2 \end{array}$$ So, $$10001_2 + 11011_2 = 101100_2$$. Would you like further details on the binary addition process or have any other questions? ### Related questions: 1. What are the steps involved in converting binary numbers to decimal? 2. How do you perform subtraction in binary? 3. Can binary numbers be multiplied in the same way as decimals? 4. What is the significance of carrying over in binary arithmetic? 5. How do you convert the binary sum back to decimal? ### Tip: When adding binary numbers, remember that carrying over happens whenever the sum of two bits is 2 or more (i.e., 1+1 = 10, which carries over 1).Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Binary Arithmetic
Binary Addition
Formulas
Binary addition formula (1+1 = 10, carry over)
Theorems
Carry over in binary arithmetic
Suitable Grade Level
Grades 6-8