| 4月28日 第2節 電子系乙組 | 誠實是我們珍視的美德， 我們喜愛「拒絕作弊，堅守正直」的你！ |
| 科目：數位電路 | （共2頁 第1頁） |
| 注意：共計五大題。每大題 20 分。 | |||||||||||||||||||||||||||||||||||
| 1. | Express each decimal number as an 8-bit number in two's complement number system. (1) -34 (2) -99 (3) -125 (4) +101 | ||||||||||||||||||||||||||||||||||
| 2. | Simplify each Boolean expression in minimum sum-of-products (SOP) form. (1) A'B(C'D'+CD)+AB(CD'+CD)+AB'C'D (2) (A'B'+AB')(CD+CD') | ||||||||||||||||||||||||||||||||||
| 3. | A majority function F(a,b,c) is generated in a combinational circuit. The output is equal to 1, if the input variables a, b, and c have more 1's than 0's. The output is 0 otherwise. (1) Derive the truth table and the simplified Boolean equation for F(a,b,c). (2) Implement F with a 4-to-1 MUX (multiplexer) shown below. Suppose that a is applied to Si, and b is applied to S0. In addition to the 4-to-1 MUX, you may use only 0, 1, NOT, OR, and AND gates.  |
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| 4. |
Minimize the number of states of the finite state machine as shown in the following state/output table.
(1) List the equivalence classes. (2) Show the minimized state machine by using state/output table. | ||||||||||||||||||||||||||||||||||
| 5. | Design a binary counter with the following binary sequence: 0, 1, 2, 3, 4, 5, 6 and repeat. Use natural binary encoding and three JK flip-flops as memory elements. | ||||||||||||||||||||||||||||||||||
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