Math Problem Statement

10001+11011 in binary

Solution

To add the binary numbers 10001210001_2 and 11011211011_2, 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).

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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