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 outcomes of the computations using the Long Division method: b) Determine the outcomes of the following computations by the "Long Division method" i) 347_8 ÷ 3_8 Step 1: Divide 3_8 by 3_8. The quotient is 1_8. r 1 \\ 3_8 ) 347_8 \\ -3 \\ 0 Step 2: Bring down 4_8. Divide 4_8 by 3_8. The quotient is 1_8 with a remainder of 1_8. r 11 \\ 3_8 ) 347_8 \\ -3 \\ 04 \\ -3 \\ 1 Step 3: Bring down 7_8. The new number is 17_8. Divide 17_8 by 3_8. In decimal: 17_8 = 1 × 8 + 7 = 15_10. 3_8 = 3_10. 15 ÷ 3 = 5. So, 3_8 × 5_8 = 17_8. The quotient is 5_8. r 115_8 \\ 3_8 ) 347_8 \\ -3 \\ 04 \\ -3 \\ 17 \\ -17 \\ 0 The remainder is 0_8. The outcome is 115_8. ii) 604_8 ÷ 4_8 Step 1: Divide 6_8 by 4_8. The quotient is 1_8 with a remainder of 2_8. r 1 \\ 4_8 ) 604_8 \\ -4 \\ 2 Step 2: Bring down 0_8. The new number is 20_8. Divide 20_8 by 4_8. In decimal: 20_8 = 2 × 8 + 0 = 16_10. 4_8 = 4_10. 16 ÷ 4 = 4. So, 4_8 × 4_8 = 20_8. The quotient is 4_8. r 14 \\ 4_8 ) 604_8 \\ -4 \\ 20 \\ -20 \\ 0 Step 3: Bring down 4_8. The new number is 04_8. Divide 4_8 by 4_8. The quotient is 1_8. r 141_8 \\ 4_8 ) 604_8 \\ -4 \\ 20 \\ -20 \\ 04 \\ -4 \\ 0 The remainder is 0_8. The outcome is 141_8. iii) 333_16 ÷ 7_16 Hexadecimal values: A=10, B=11, C=12, D=13, E=14, F=15. Step 1: 7_16 cannot divide 3_16. Consider 33_16. In decimal: 33_16 = 3 × 16 + 3 = 51_10. 7_16 = 7_10. 51 ÷ 7 = 7 with a remainder of 2. So, 7_16 × 7_16 = 49_10 = 31_16. The quotient is 7_16. r 7 \\ 7_16 ) 333_16 \\ -31 \\ 2 Step 2: Bring down 3_16. The new number is 23_16. Divide 23_16 by 7_16. In decimal: 23_16 = 2 × 16 + 3 = 35_10. 7_16 = 7_10. 35 ÷ 7 = 5. So, 7_16 × 5_16 = 35_10 = 23_16. The quotient is 5_16. r 75_16 \\ 7_16 ) 333_16 \\ -31 \\ 23 \\ -23 \\ 0 The remainder is 0_16. The outcome is 75_16. iv) 1B90_16 ÷ C_16 Hexadecimal values: A=10, B=11, C=12, D=13, E=14, F=15. C_16 = 12_10. Step 1: C_16 cannot divide 1_16. Consider 1B_16. In decimal: 1B_16 = 1 × 16 + 11 = 27_10. C_16 = 12_10. 27 ÷ 12 = 2 with a remainder of 3. So, C_16 × 2_16 = 12_10 × 2_10 = 24_10 = 18_16. The quotient is 2_16. r 2 \\ C_16 ) 1B90_16 \\ -18 \\ 3 Step 2: Bring down 9_16. The new number is 39_16. Divide 39_16 by C_16. In decimal: 39_16 = 3 × 16 + 9 = 57_10. C_16 = 12_10. 57 ÷ 12 = 4 with a remainder of 9. So, C_16 × 4_16 = 12_10 × 4_10 = 48_10 = 30_16. The quotient is 4_16. r 24 \\ C_16 ) 1B90_16 \\ -18 \\ 39 \\ -30 \\ 9 Step 3: Bring down 0_16. The new number is 90_16. Divide 90_16 by C_16. In decimal: 90_16 = 9 × 16 + 0 = 144_10. C_16 = 12_10. 144 ÷ 12 = 12. So, C_16 × C_16 = 12_10 × 12_10 = 144_10 = 90_16. The quotient is C_16.