DieselShip's Online Content Library

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

For this logic system:

(i) produce an unsimplified Boolean expression for output X; (2)

(ii) use a Karnaugh map or Boolean algebra to simplify as fully as possible, the expression for X obtained in Q9(a)(i); (5)

(iii) use the expression for X obtained in Q9(a)(ii) to produce the logic circuit using only NAND gates, crossing out any redundant gates. (3)

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

(i) the binary operation 10111 X 1101; (1)

(ii) the conversion of 1101101₂ to decimal form; (1)

(iii) the conversion of 3AB₁₆ to binary form; (2)

(iv) the hexadecimal operation AD8F + DECC. (2)