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Q9 (a) The truth table for a logic system with inputs A, B and C, and output X, is shown in Table Q9(a).

Table Q9(a)

(i) Use Table Q9(a) to produce an unsimplified Boolean expression for X in terms of A, B and C. (3)

(ii) Use Boolean algebra or a Karnaugh map to show that X = A̅B  + A̅C . (3)

(iii) Produce the logic circuit for the system using NOT, AND and OR gates. (4)

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

(i) the binary operation 10111 x 1101; (2)

(ii) the hexadecimal operation BEFA + C4D7; (2)

(iii) the conversion of A3DC₁₆ to decimal. (2)