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https://hackmd.io/@IMOK/Lab2
講師: 賴昱有
由2個或多個and(以 * 號表示)組合而成的項透過or(以+號表示)連結而成
注意! 是不一樣的
由2個或多個or(以 + 號表示)組合而成的項透過and(以*號表示)連結而成
※化成標準形式的好處
標準形式布林函數屬於「雙階層執行電路」,即只經過兩層,如此可統一邏輯閘延遲時間。
許多logic circuit在最初設計的時候過於複雜
簡化和最佳化數位邏輯電路
可以減少電路的複雜性、降低功耗、提高性能和可靠性(減少耗費的電晶體)。
※使用真值表可以檢驗是否為等效電路
A | B | C | F |
---|---|---|---|
0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 |
0 | 1 | 0 | 0 |
0 | 1 | 1 | 0 |
1 | 0 | 0 | 1 |
1 | 0 | 1 | 1 |
1 | 1 | 0 | 0 |
1 | 1 | 1 | 1 |
A | B | C | F |
---|---|---|---|
0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 |
0 | 1 | 0 | 0 |
0 | 1 | 1 | 0 |
1 | 0 | 0 | 1 |
1 | 0 | 1 | 1 |
1 | 1 | 0 | 0 |
1 | 1 | 1 | 1 |
最直接的方式為使用德摩根定律(DeMorgan's Laws)、分配律(Distributive Law)等..進行代數化簡
※補充:須注意XOR及XNOR的展開比較特別
缺點: 無法輕易判斷使否為最簡表達式
第二定律(OR的德摩根定律):對於任意兩個布林表達式A和B,其OR運算(或運算)的德摩根定律可以表述為:
¬(A ∨ B) = (¬A) ∧ (¬B)
設計組合邏輯電路最簡單的方法是使用真值表。
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1. Groupings can contain only 1s; no 0s.(翻譯:只能圈選minterm為1的cell)
2. Groups can be formed only at right angles; diagonal groups are not allowed.(翻譯:不可以斜的)
3. The number of 1s in a group must be a power of 2-even if it contains a single 1.
(翻譯:每個組要圈選到2的x次方個cell)
4. The groups must be made as large as possible.(翻譯:越大越好)
5. Groups can overlap and wrap around the sides of the Karnaugh map.(翻譯:可以跨過邊界)
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For the questions below, please write down the Boolean functions,truth tables,
the simplification method and process, and the final circuit using LogicCircuit.
Design a logic circuit which implements a majority voter.
There are 3 people A, B, and C.
If 2 out of the three people votes for an yes, i.e., a logic 1, then the output is 1.
Otherwise, output 0.
Design a logic circuit that is to produce a 1 or HIGH
output when the voltage is greater than 6V.
(represented by a four-bit binary number ABCD)