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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)

Produce EACH of the following for the logic system:

(i) a Boolean expression in its simplest form; (4)

(ii) the logic circuit, with the minimum number of parts (3)

(iii) the logic circuit, using only NAND gates. (3)

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

(i) the binary operation 10111011 – 1010111; (1)

(ii) the hexagonal operation CD4B + EA7;     (2)

(iii) the conversion of B5EA₁₆ to decimal ; (2)

(iv) the conversion of 111001100111₂ to hexadecimal. (1)