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 are the solutions for Section A: SECTION A 1. Find the difference between the roman numeration MMLXV and MCM. Hence convert the difference into binary. Step 1: Convert MMLXV to decimal. MMLXV = M + M + L + X + V = 1000 + 1000 + 50 + 10 + 5 = 2065 Step 2: Convert MCM to decimal. MCM = M + CM = 1000 + (1000 - 100) = 1000 + 900 = 1900 Step 3: Find the difference. Difference = 2065 - 1900 = 165 Step 4: Convert the difference (165) to binary. 165 ÷ 2 = 82 R 1 82 ÷ 2 = 41 R 0 41 ÷ 2 = 20 R 1 20 ÷ 2 = 10 R 0 10 ÷ 2 = 5 R 0 5 ÷ 2 = 2 R 1 2 ÷ 2 = 1 R 0 1 ÷ 2 = 0 R 1 Reading the remainders from bottom to top: The difference in binary is 10100101_2. 2. Convert the Egyptian numeral ||||| into roman numerals. Step 1: Determine the decimal value of the Egyptian numeral. The Egyptian numeral ||||| represents: (heel-bone) = 10 | (single stroke) = 1 So, ||||| = (3 × 10) + (5 × 1) = 30 + 5 = 35. Step 2: Convert the decimal value to Roman numerals. 35 = 30 + 5 = XXX + V = XXXV. The Roman numeral is XXXV. 3. Carry out the operation indicated in each of the following: i. 334_5 + 224_5 Step 1: Add the numbers in base 5. ` 334_5 + 224_5 ------- ` Starting from the rightmost digit: 4_5 + 4_5 = 8_10 = 1 × 5 + 3 = 13_5. Write down 3, carry over 1. 3_5 + 2_5 + 1_5 (carry) = 6_10 = 1 × 5 + 1 = 11_5. Write down 1, carry over