5. [20 marks] Integer Multiplication II. a) First, show that, regardless of the initial n-bit value of the accumulator, the fused multiply-add result of two n-bit natural-number operands is always representable in 2n bits. Second, starting from the largest possible FMA result, what is the largest n-bit number that can _still_ be added without producing overflow? Third, if n = 16, what is this largest n-bit number? b) A modular-adder device 'M' operates with 16-bit registers. You give it two 16-bit natural numbers 'a' and 'b'. You know 'a', but you don't know 'b'. The device adds them, divides by 2^16, keeps the quotient 'q' a secret, and publishes the remainder 'r'. Hint: Before answering, experiment with small addition tables. i) If a = 19,473 and r = 62,787, what are 'b' and 'q'? ii) If a = 42,444 and r = 13,804, what are 'b' and 'q'?