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
Step 1: Convert 310_10 to base 2. Repeatedly divide the number by 2 and record the remainders (read remainders from last to first). 310 &÷ 2 = 155 \ remainder\ 0, \\ 155 &÷ 2 = 77 \ remainder\ 1, \\ 77 &÷ 2 = 38 \ remainder\ 1, \\ 38 &÷ 2 = 19 \ remainder\ 0, \\ 19 &÷ 2 = 9 \ remainder\ 1, \\ 9 &÷ 2 = 4 \ remainder\ 1, \\ 4 &÷ 2 = 2 \ remainder\ 0, \\ 2 &÷ 2 = 1 \ remainder\ 0, \\ 1 &÷ 2 = 0 \ remainder\ 1. Remainders from bottom to top: 100110110_2. 310_10 = 100110110_2 100110110_2 Step 2: Convert 310_10 to base 8. 310 &÷ 8 = 38 \ remainder\ 6, \\ 38 &÷ 8 = 4 \ remainder\ 6, \\ 4 &÷ 8 = 0 \ remainder\ 4. Remainders from bottom to top: 466_8. 310_10 = 466_8 466_8 Step 3: Convert 310_10 to base 16. 310 &÷ 16 = 19 \ remainder\ 6, \\ 19 &÷ 16 = 1 \ remainder\ 3, \\ 1 &÷ 16 = 0 \ remainder\ 1. Remainders from bottom to top: 136_16. 310_10 = 136_16 136_16 Step 4: Convert 2510_10 to base 2. 2510 &÷ 2 = 1255 \ remainder\ 0, \\ 1255 &÷ 2 = 627 \ remainder\ 1, \\ 627 &÷ 2 = 313 \ remainder\ 1, \\ 313 &÷ 2 = 156 \ remainder\ 1, \\ 156 &÷ 2 = 78 \ remainder\ 0, \\ 78 &÷ 2 = 39 \ remainder\ 0, \\ 39 &÷ 2 = 19 \ remainder\ 1, \\ 19 &÷ 2 = 9 \ remainder\ 1, \\ 9 &÷ 2 = 4 \ remainder\ 1, \\ 4 &÷ 2 = 2 \ remainder\ 0, \\ 2 &÷ 2 = 1 \ remainder\ 0, \\ 1 &÷ 2 = 0 \ remainder\ 1. Remainders from bottom to top: 100111001110_2. 2510_10 = 100111001110_2 100111001110_2 Step 5: Convert 2510_10 to base 8. 2510 &÷ 8 = 313 \ remainder\ 6, \\ 313 &÷ 8 = 39 \ remainder\ 1, \\ 39 &÷ 8 = 4 \ remainder\ 7, \\ 4 &÷ 8 = 0 \ remainder\ 4. Remainders from bottom to top: 4716_8. 2510_10 = 4716_8 4716_8 Step 6: Convert 2510_10 to base 16. 2510 &÷ 16 = 156 \ remainder\ 14 \ (E), \\ 156 &÷ 16 = 9 \ remainder\ 12 \ (C), \\ 9 &÷ 16 = 0 \ remainder\ 9. Remainders from bottom to top: 9CE_16. 2510_10 = 9CE_16 9CE_16 Step 7: Convert 282_10 to base 2. 282 &÷ 2 = 141 \ remainder\ 0, \\ 141 &÷ 2 = 70 \ remainder\ 1, \\ 70 &÷ 2 = 35 \ remainder\ 0, \\ 35 &÷ 2 = 17 \ remainder\ 1, \\ 17 &÷ 2 = 8 \ remainder\ 1, \\ 8 &÷ 2 = 4 \ remainder\ 0, \\ 4 &÷ 2 = 2 \ remainder\ 0, \\ 2 &÷ 2 = 1 \ remainder\ 0, \\ 1 &÷ 2 = 0 \ remainder\ 1. Remainders from bottom to top: 100011010_2. 282_10 = 100011010_2 100011010_2 Step 8: Convert 282_10 to base 8. 282 &÷ 8 = 35 \ remainder\ 2, \\ 35 &÷ 8 = 4 \ remainder\ 3, \\ 4 &÷ 8 = 0 \ remainder\ 4. Remainders from bottom to top: 432_8. 282_10 = 432_8 432_8 Step 9: Convert 282_10 to base 16. 282 &÷ 16 = 17 \ remainder\ 10 \ (A), \\ 17 &÷ 16 = 1 \ remainder\ 1, \\ 1 &÷ 16 = 0 \ remainder\ 1. Remainders from bottom to top: 11A_16. 282_10 = 11A_16 11A_16 Step 10: Convert 4990_10 to base 2. 4990 &÷ 2 = 2495 \ remainder\ 0, \\ 2495 &÷ 2 = 1247 \ remainder\ 1, \\ 1247 &÷ 2 = 623 \ remainder\ 1, \\ 623 &÷ 2 = 311 \ remainder\ 1, \\ 311 &÷ 2 = 155 \ remainder\ 1, \\ 155 &÷ 2 = 77 \ remainder\ 1, \\ 77 &÷ 2 = 38 \ remainder\ 1, \\ 38 &÷ 2 = 19 \ remainder\ 0, \\ 19 &÷ 2 = 9 \ remainder\ 1, \\ 9 &÷ 2 = 4 \ remainder\ 1, \\ 4 &÷ 2 = 2 \ remainder\ 0, \\ 2 &÷ 2 = 1 \ remainder\ 0, \\ 1 &÷ 2 = 0 \ remainder\ 1. Remainders from bottom to top: 1001101111110_2. 4990_10 = 1001101111110_2 1001101111110_2 Step 11: Convert 4990_10 to base 8. 4990 &÷ 8 = 623 \ remainder\ 6, \\ 623 &÷ 8 = 77 \ remainder\ 7, \\ 77 &÷ 8 = 9 \ remainder\ 5, \\ 9 &÷ 8 = 1 \ remainder\ 1, \\ 1 &÷ 8 = 0 \ remainder\ 1. Remainders from bottom to top: 11576_8. 4990_10 = 11576_8 11576_8 Step 12: Convert 4990_10 to base 16. 4990 &÷ 16 = 311 \ remainder\ 14 \ (E), \\ 311 &÷ 16 = 19 \ remainder\ 7, \\ 19 &÷ 16 = 1 \ remainder\ 3, \\ 1 &÷ 16 = 0 \ remainder\ 1. Remainders from bottom to top: 137E_16. 4990_10 = 137E_16 137E_16