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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)

For this logic system:

(i) produce an unsimplified Boolean expression for output X: (1)

(ii) use a Karnaugh map or Boolean algebra to simplify as fully as possible, the expression for x obtained in Q9(a) (i); (3)

(iii) use the expression for X obtained in Q9(a)(ii) to produce the logic circuit using NOT, AND and OR gates. (3)

(b) Simplify, as fully as possible, the following Boolean expression: (3)

(c) Determine EACH of the following. without using a calculator conversion function:

(i) the conversion of 95₁₀ to binary: (2)

(ii) the conversion of 1110110110011₂ to hexadecimal; (2)

(iii) the hexadecimal operation E8BA - BC3D. (2)