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Q9 (a) Determine EACH of the following, without using a calculator conversion function:

(i) the conversion of 1275₁₀ to hexadecimal; (2)

(ii) the hexadecimal operation EB4C – A5DF. (2)

(b) The truth table for a logic system with inputs P, Q and R, and output X, is shown in Table Q9(a)

Table Q9(b)

Produce EACH of the following for the logic system:

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

(ii) the equivalent logic circuit with the minimum number of gates; (3)

(iii) the equivalent logic circuit using only NAND gates, (crossing out any redundant gates). (5)