Q9 (a) Determine EACH of the following, without using a calculator conversion function:
(i) the binary operation 1011001 – 100101; (1)
(ii) the conversion of 7910 to binary; (1)
(iii) the hexadecimal operation DFC5 + 3A8B; (2)
(iv) the conversion of 176910 to hexadecimal. (2)
(b) The truth table for a logic system with inputs A, Band C, and output X, is shown in Table Q9(b):
| A | B | C | X |
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 0 |
Table (b)
(i) Use Table Q9(b) to write down the un simplified Boolean expression for X in terms of A, B and C. (2)
(ii) Simplify the expression in Q9(b)(i) as fully as possible, using Karnaugh map and/or the rules of Boolean algebra. (2)
(iii) Produce the logic circuit for the system, with the minimum number of gates. (3)
(c) Simplify, as fully as possible, the following Boolean expression:
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