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 to your number base problems: 1) Convert into Bases i) Convert 1101001.1011_2 to Base 10. Step 1: Convert the integer part 1101001_2 to base 10. 1101001_2 = (1 × 2^6) + (1 × 2^5) + (0 × 2^4) + (1 × 2^3) + (0 × 2^2) + (0 × 2^1) + (1 × 2^0) = (1 × 64) + (1 × 32) + (0 × 16) + (1 × 8) + (0 × 4) + (0 × 2) + (1 × 1) = 64 + 32 + 0 + 8 + 0 + 0 + 1 = 105_10 Step 2: Convert the fractional part 0.1011_2 to base 10. 0.1011_2 = (1 × 2^-1) + (0 × 2^-2) + (1 × 2^-3) + (1 × 2^-4) = (1 × 0.5) + (0 × 0.25) + (1 × 0.125) + (1 × 0.0625) = 0.5 + 0 + 0.125 + 0.0625 = 0.6875_10 Step 3: Combine the integer and fractional parts. 105_10 + 0.6875_10 = 105.6875_10 The converted number is 105.6875_10. ii) Convert 236.725_10 to Base 7. Step 1: Convert the integer part 236_10 to base 7 using successive division. 236 ÷ 7 = 33 remainder 5 33 ÷ 7 = 4 remainder 5 4 ÷ 7 = 0 remainder 4 Reading the remainders from bottom up gives 455_7. Step 2: Convert the fractional part 0.725_10 to base 7 using successive multiplication. 0.725 × 7 = 5.075 integer part is 5 0.075 × 7 = 0.525 integer part is 0 0.525 × 7 = 3.675 integer part is 3 0.675 × 7 = 4.725 integer part is 4 (We can stop here or continue, as the pattern 0.725 repeats, leading to 5034...) Reading the integer parts from top down gives 0.5034..._7. Step 3: Combine the integer and fractional parts. 236.725_10 ≈ 455.5034_7 The converted number is approximately 455.5034_7. 2) Calculate the following i) Calculate 46C1_16 + 77BF_16 We perform hexadecimal addition column by column, remembering that A=10, B=11, C=12, D=13, E=14, F=15. Step 1: Add the rightmost column (1s place). 1_16 + F_16 = 1 + 15 = 16_10 16_10 = 1 × 16 + 0 write down 0, carry over 1 Step 2: Add the second column from the right (16s place). C_16 + B_16 + 1 (carry) = 12 + 11 + 1 = 24_10 24_10 = 1 × 16 + 8 write down 8, carry over 1 Step 3: Add the third column from the right (256s place). 6_16 + 7_16 + 1 (carry) = 6 + 7 + 1 = 14_10 14_10 = E_16 write down E, carry over 0 Step 4: Add the leftmost column (4096s place). 4_16 + 7_16 + 0 (carry) = 4 + 7 + 0 = 11_10 11_10 = B_16 write down B Combining the results: 46C1_16 + 77BF_16 = BE80_16 The sum is BE80_16. 3 done, 2 left today. You're making progress.