課程名稱︰邏輯電路
課程性質︰分組必修
課程教師︰黃乾鋼
開課學院：工學院
開課系所︰工程科學與海洋工程學系
考試日期（年月日）︰2006/11/16
考試時限（分鐘）：180
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
(please DON't provide your answers ONLY.
Inverter gate is always allowed in logic circuit diagram.)
1. (10%) Brief explanation of Terminologies:
(a) Gray code (Give a 3-bit Gray code example).
(b) Duality principle
(c) DeMorgan's theorem (Give the dual form)
(d) Canonical Form vx.Stand Form
(e) Positive and Negative Logic
2. (5%)
Find the 11's and 12's complement of 92A5(12)
3. (5%)
How many different Boolean functions can be composed using n Boolean
variables?
4. (10%)
Prove the following equations algebraically, that is , using Postulates
and Theorems of boolean algebra.
(a) xy+x'y+yz=xy+x'z
(b) (x+y)(x'+z)(y+z)=(x+y)(x'+z)
5. (10%) F(A,B,C,D)=ABC'+AB'D+BCD
(a) simplify the boolean function F to sum-of-minterms and
product-of-maxterms
(b) simplify the boolean function F' to sum-of-products and
products-of-sums.
6. (10%) F(x,y,z)=Σ(2,3,4),d(x,y,z)=Σ(0,1,5)
(a) simplify the above boolean function F, together with the don;t-care
conditions d, ad express the simplified function in sum of product form.
(b) implement Fwith two-level NAND gates.
7. (10%) F(A,B,C,D)=Σ(0,4,8,9,10,11,12,14)
(a) implement F with two-level NOR gates
(b) implement F' with OR-NAND gates
8. (10%)
consider the 4 types of gates: AND,OR,NAND,NOR. list the 8 degenerate
forms of two-level combinations of gates.Select one of the 8 degenerate
forms, and prove it can degenerate into one level.
9. (5%)
Give the implement of 2-input exclusive -OR operation with 4NAND gates.
Prove the implementation can be simplified to the exclusive-OR operation.
10.(10%)
(a)obtain the simplified boolean expressions from outputs F and G in terms
of the input variables in the circuit of fig 1 in Sum of product form.
(b)Consider the truth table.
A───Inverter──┬─────NAND──────AND─────F
│ ┌──┘ ┌──┘
├─────OR────┤
B──┐ │ │ │ └──┐
AND──────│─────┘ AND─────G
C──┘ │ │ │
│ │ │
D─────────NAND─┴──────────┘
Fig 1
11.(5%) Design the half adder
(a) construct the truth table and give the simplified boolean expression
(b) show the implementation (no more than 2 gates)
12.(10%) Design the excess-3 to BCD converter
(a) Construct the truth table and give the simplified boolean expression
(b) show the implementation (using AND-OR implementation).
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