5. [20 marks] Integer Multiplication II. a) 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. Now, suppose n = 16. Starting from the largest possible FMA result, what is the hexadecimal representation of the largest n = 16-bit number that can _still_ be added without producing overflow? b) A modular-adder device 'M' operates with 16-bit registers. You give it two 16-bit natural numbers 'a' and 'b'. It 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 = 23,979 and r = 63,400, what are 'b' and 'q'? ii) If a = 33,472 and r = 8,047, what are 'b' and 'q'?