This computer science problem involves algorithmic thinking and programming concepts. The solution below explains the approach, logic, and implementation step by step.
ScanSolve AI Answer
Okay CØTBØJ, let's tackle these hexadecimal subtraction problems. Hexadecimal (base 16) uses digits 0-9 and letters A-F, where: A = 10 B = 11 C = 12 D = 13 E = 14 F = 15 When you need to borrow in hexadecimal subtraction, you borrow 1 from the next column to the left, which adds 16 to the current column's value. --- Problem (c): EBA_16 - 2E_16 We'll subtract column by column, from right to left. Step 1: Subtract the rightmost column (16⁰ place). We need to calculate A_16 - E_16. In decimal, this is 10 - 14. Since 10 < 14, we need to borrow from the next column. Borrow 1 from B in the 16^1 place. B (11_10) becomes A (10_10). The borrowed 1 is equivalent to 16_10 in the current column. So, A (10_10) becomes 10 + 16 = 26_10. Now, subtract: 26_10 - E_16 = 26_10 - 14_10 = 12_10. In hexadecimal, 12_10 is C. So, the rightmost digit is C. Step 2: Subtract the middle column (16¹ place). The B in EBA_16 became A after borrowing. We need to calculate A_16 - 2_16. In decimal, this is 10 - 2 = 8_10. In hexadecimal, 8_10 is 8. So, the middle digit is 8. Step 3: Subtract the leftmost column (16² place). We need to calculate E_16 - 0_16 (since there's no digit in the 16^2 place for 2E_16). In decimal, this is 14 - 0 = 14_10. In hexadecimal, 14_10 is E. So, the leftmost digit is E. Combining the results: EBA_16 - 2E_16 = E8C_16 --- Problem (d): BABA_16 - EBA_16 We'll subtract column by column, from right to left. Step 1: Subtract the rightmost column (16⁰ place). We need to calculate A_16 - A_16. In decimal, this is 10 - 10 = 0_10. So, the rightmost digit is 0. Step 2: Subtract the second column from the right (16¹ place). We need to calculate B_16 - B_16. In decimal, this is 11 - 11 = 0_10. So, the second digit from the right is 0. Step 3: Subtract the third column from the right (16² place). We need to calculate A_16 - E_16. In decimal, this is 10 - 14. Since 10 < 14, we need to borrow from the next column. Borrow 1 from B in the 16^3 place. B (11_10) becomes A (10_10). The borrowed 1 is equivalent to 16_10 in the current column. So, A (10_10) becomes 10 + 16 = 26_10. Now, subtract: 26_10 - E_16 = 26_10 - 14_10 = 12_10. In hexadecimal, 12_10 is C. So, the third digit from the right is C. Step 4: Subtract the leftmost column (16³ place). The B in BABA_16 became A after borrowing. We need to calculate A_16 - 0_16 (since there's no digit in the 16^3 place for EBA_16). In decimal, this is 10 - 0 = 10_10. In hexadecimal, 10_10 is A. So, the leftmost digit is A. Combining the results: BABA_16 - EBA_16 = AC00_16 Drop the next question.