Next Page Uestion 12 (1 point) In binary subtraction what is \( 1100101100101000_{2}-1001111001011011_{2} \) ? \( 10110011001101_{3} \)

To perform the binary subtraction \( 1100101100101000_{2} - 1001111001011011_{2} \), we can follow the standard binary subtraction method, borrowing when necessary. Let's break it down step by step: 1. Align the numbers for subtraction: ``` 1100101100101000 - 1001111001011011 ``` 2. Start subtracting from the rightmost bit: ``` 1100101100101000 - 1001111001011011 --------------------- ``` - **Column 1**: \( 0 - 1 \) (borrow from the next column) - Result: \( 1 \) (after borrowing) - **Column 2**: \( 0 - 1 \) (borrow again) - Result: \( 1 \) (after borrowing) - **Column 3**: \( 0 - 0 \) - Result: \( 0 \) - **Column 4**: \( 1 - 1 \) - Result: \( 0 \) - **Column 5**: \( 0 - 1 \) (borrow) - Result: \( 1 \) (after borrowing) - **Column 6**: \( 1 - 1 \) - Result: \( 0 \) - **Column 7**: \( 1 - 1 \) - Result: \( 0 \) - **Column 8**: \( 0 - 0 \) - Result: \( 0 \) - **Column 9**: \( 0 - 1 \) (borrow) - Result: \( 1 \) (after borrowing) - **Column 10**: \( 1 - 0 \) - Result: \( 1 \) - **Column 11**: \( 0 - 0 \) - Result: \( 0 \) - **Column 12**: \( 1 - 1 \) - Result: \( 0 \) - **Column 13**: \( 1 - 0 \) - Result: \( 1 \) - **Column 14**: \( 1 - 0 \) - Result: \( 1 \) - **Column 15**: \( 1 - 0 \) - Result: \( 1 \) - **Column 16**: \( 1 - 0 \) - Result: \( 1 \) Putting it all together, we get: ``` 1100101100101000 - 1001111001011011 --------------------- 0010110010001111 ``` Thus, the result of the binary subtraction \( 1100101100101000_{2} - 1001111001011011_{2} \) is \( 0010110010001111_{2} \). Now, let's convert this binary result to base 3: 1. Convert \( 0010110010001111_{2} \) to decimal: - \( 0 \times 2^{15} + 0 \times 2^{14} + 1 \times 2^{13} + 0 \times 2^{12} + 1 \times 2^{11} + 1 \times 2^{10} + 0 \times 2^{9} + 0 \times 2^{8} + 1 \times 2^{7} + 0 \times 2^{6} + 0 \times 2^{5} + 1 \times 2^{4} + 1 \times 2^{3} + 1 \times 2^{2} + 1 \times 2^{1} + 1 \times 2^{0} \) - \( = 0 + 0 + 8192 + 0 + 2048 + 1024 + 0 + 0 + 128 + 0 + 0 + 16 + 8 + 4 + 2 + 1 \) - \( = 0 + 8192 + 2048 + 1024 + 128 + 16 + 8 + 4 + 2 + 1 = 0 + 8192 + 2048 + 1024 + 128 + 16 + 8 + 4 + 2 + 1 = 0 + 8192 + 2048 + 1024 + 128 + 16 + 8 + 4 + 2 + 1 = 0 + 8192