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Q9) The logic circuit shown in fig Q9(a) has three inputs A,B and C, and one output X.

Produce EACH of the following for this circuit:

(i) an unsimplified Boolean expression for X (4)

(ii) the truth table, by simplifying as fully as possible the Boolean expression obtained for X in Q9a) (i). or otherwise (4)

(iii) the equivalent circuit with the minimum number of gates. (2)

(b) Determine EACH of the following, without the use of a calculator conversion function:

(i) the conversion of 101110₂ to decimal (1)

(ii) the conversion of DABE₁₆ to decimal (2)

(iii) the value, in hexadecimal form, of the operation AB₁₆ ÷ 10011₂. (3)