1. **Convert (85.375)₁₀ to binary (base 2):** Step 1: Convert the integer part 85 to binary. - Divide 85 by 2 repeatedly and record remainders: 85 ÷ 2 = 42 remainder 1 42 ÷ 2 = 21 remainder 0 21 ÷ 2 = 10 remainder 1 10 ÷ 2 = 5 remainder 0 5 ÷ 2 = 2 remainder 1 2 ÷ 2 = 1 remainder 0 1 ÷ 2 = 0 remainder 1 - Reading remainders from bottom to top: 1010101 Step 2: Convert the fractional part 0.375 to binary. - Multiply 0.375 by 2: 0.375 × 2 = 0.75 → integer part 0 - Multiply 0.75 by 2: 0.75 × 2 = 1.5 → integer part 1 - Multiply 0.5 by 2: 0.5 × 2 = 1.0 → integer part 1 - Fractional binary digits: 011 Step 3: Combine integer and fractional parts: $$85.375_{10} = 1010101.011_2$$ 2. **Convert (132)₄ to base 6:** Step 1: Convert (132)₄ to decimal. - Digits: 1, 3, 2 (from left to right) - Calculate value: $$1 \times 4^2 + 3 \times 4^1 + 2 \times 4^0 = 1 \times 16 + 3 \times 4 + 2 \times 1 = 16 + 12 + 2 = 30$$ Step 2: Convert decimal 30 to base 6. - Divide 30 by 6 repeatedly: 30 ÷ 6 = 5 remainder 0 5 ÷ 6 = 0 remainder 5 - Reading remainders from bottom to top: 50 Step 3: Final result: $$(132)_4 = (50)_6$$