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
The image shows the process of converting the decimal number 164_10 to its binary equivalent using repeated division by 2. Let's verify the steps shown in your work: Step 1: Divide 164 by 2. 164 ÷ 2 = 82 with a remainder of 0. (Correct) Step 2: Divide 82 by 2. 82 ÷ 2 = 41 with a remainder of 0. (Correct) Step 3: Divide 41 by 2. 41 ÷ 2 = 20 with a remainder of 1. (Correct) Step 4: Divide 20 by 2. 20 ÷ 2 = 10 with a remainder of 0. (Correct) Step 5: Divide 10 by 2. 10 ÷ 2 = 5 with a remainder of 0. (Correct) Step 6: Divide 5 by 2. 5 ÷ 2 = 2 with a remainder of 1. (Correct) Step 7: Divide 2 by 2. 2 ÷ 2 = 1 with a remainder of 0. (Correct) Step 8: Divide 1 by 2. 1 ÷ 2 = 0 with a remainder of 1. (Correct) To obtain the binary number, you read the remainders from bottom to top. The remainders are: 1, 0, 1, 0, 0, 1, 0, 0. Therefore, the correct binary representation of 164_10 is 10100100_2. Your division steps are all correct. However, the final binary number you wrote on the right side of the page, (0010010)_2, is incorrect. It seems you might have missed the leftmost '1' and reversed the order of some digits. The correct final answer is 10100100_2. 3 done, 2 left today. You're making progress.