First, convert to base 10: 100110₂ = 38₁₀, 111₂ = 7₁₀. 38 ÷ 7 = 5 remainder 3. 5₁₀ = 101₂, remainder 3₁₀ = 11₂. But more precisely, 38 ÷ 7 = 5.428..., but in integer division, it's 5 remainder 3. The question likely expects integer division. Let's perform binary long division: 100110₂ ÷ 111₂ = 110₂ (6₁₀) with a remainder. Actually, 111₂ * 110₂ = 111₂ * (100₂ + 10₂) = 11100₂ + 1110₂ = 101010₂, which is too big. Let's recalc: 111₂ * 101₂ = 111₂ * (100₂ + 1₂) = 11100₂ + 111₂ = 100011₂. 100110₂ - 100011₂ = 11₂ remainder. So quotient = 101₂, remainder = 11₂. The answer is 101₂ remainder 11₂. But the instruction says 'giving your answer in base two', likely meaning the quotient. So answer is 101₂.

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• loveness Phiri – 1084 pts

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