This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here is the solution to your question: b) Using two's complement, work out 37_10 - 17_10, giving your answer in decimal notation. (4 marks) This is equivalent to 37_10 + (-17_10). We will use an 8-bit representation. Step 1: Convert 37_10 to 8-bit binary. 37_10 = 00100101_2 Step 2: Convert 17_10 to 8-bit binary. 17_10 = 00010001_2 Step 3: Find the two's complement of 17_10 to represent -17_10. Original binary for 17_10: 00010001_2 One's complement (invert all bits): 11101110_2 Two's complement (add 1 to one's complement): c 11101110_2 \\ + 00000001_2 \\ 11101111_2 So, -17_10 in 8-bit two's complement is 11101111_2. Step 4: Add 37_10 and the two's complement of -17_10. c 00100101_2 (37_10) \\ + 11101111_2 (-17_10 in two's complement) \\ 1 \ 00100100_2 The leftmost '1' is a carry-out. In two's complement arithmetic, a carry-out from the most significant bit is discarded. Step 5: The result is 00100100_2. Convert this binary number back to decimal. 0 × 2^7 + 0 × 2^6 + 1 × 2^5 + 0 × 2^4 + 0 × 2^3 + 1 × 2^2 + 0 × 2^1 + 0 × 2^0 = 0 + 0 + 32 + 0 + 0 + 4 + 0 + 0 = 36_10 The final answer is 36_10.