我正在进行一项教科书练习，要求“使用布尔代数法则最小化以下布尔表达式，然后在不使用NOT门的情况下为其开发逻辑电路”。
表达式是X =（不是A）和（不是B或C）或不是（C或A）
首先，我试图最小化这个等式。 我使用左侧的分配法将（不是A）和（不是B或C）转换为（不是A而不是B）或（不是A和C）。
因此遵循这个定律，新的等式是（不是A而不是B）或（不是A和C）或（不是C而不是A）。
在（（不是A和C）OR（非C和非A））的右侧分组，表明还有另一个法则规定（AB + A（NOT B）= A）。
我在这里使用这个法律（称这个法律？）来简化整个表达式，简单地说就是NOT（A）。
所以新的等式是（不是A而不是B）或（不是A）。
我使用冗余定律，它表明（A + AB = A），将整个表达式改为NOT（A）。
在这个最小化之后，我已经成功地将整个方程最小化为X = NOT（A）。 真值表显示它们在功能上是等价的。
我的两个问题是1.我看到的地方？ 法律，我已经搜索了这个法律的名称，但一直找不到。 是否有法律名称（AB + A（非B）= A）？ 2.如果函数不是（A），我不确定如何在不使用NOT门的情况下设计逻辑电路？ 我在想，也许NAND门可以工作，但那些有逆变器。 如果它要求不使用NOT门，那么使用NAND门仍然有效吗？
感谢您的任何帮助。
I am working on a textbook exercise that asks to "Minimize the following boolean expression using boolean algebraic laws, and then develop a logic circuit for it WITHOUT using a NOT gate".
The expression is X= (NOT A) AND (NOT B OR C) OR NOT(C OR A)
First, I attempt to minimize this equation. I use distribute law of the left hand side to turn (NOT A) AND (NOT B OR C) to (NOT A AND NOT B) OR (NOT A AND C).
So following this law, the new equation is (NOT A AND NOT B) OR (NOT A AND C) OR (NOT C AND NOT A).
Grouping at the right hand side of ((NOT A AND C) OR (NOT C AND NOT A)), shows that there is another law that states (AB + A(NOT B) = A).
I use this LAW (Call this law ?) here to simplify the entire expression to simply NOT(A).
So the new equation is (NOT A AND NOT B) OR (NOT A).
I use the redundancy law, which states that (A + AB = A), to change the entire expression to simply NOT(A).
Following this minimization, I have successfully minimized the entire equation to X=NOT(A). Truth tables show they are functionally equivalent.
My two questions are 1. The area where I saw ? Law, I have searched for a name for this law but have not been able to find one. Is there a name for the law (AB + A(NOT B) = A)? 2. If the function is NOT(A), I am not sure how one could design a logic circuit without using a NOT gate? I was thinking that maybe a NAND gate could work, but those have inverters. If it asks to not use a NOT gate, is it still valid to use a NAND gate?
Thank you for any help.
最满意答案
AB + A(NOT B) = A没有名称，该等式只是分布定律 AB + A(NOT B) = A(B + NOT B)的结果， B + NOT B = TRUE的事实。
关于你对NAND的关注，是的，你需要使用它，因为没有办法从OR和AND得到NOT 。
There is no name for AB + A(NOT B) = A, the equation is just a consequence of the distribution law AB + A(NOT B) = A(B + NOT B) and the fact that B + NOT B = TRUE.
Regarding your concern about NAND, yes you need to used it because there is no way to get NOT from just OR and AND.
布尔表达式 - 最小化和规律(Boolean Expression- Minimization and Law)我正在进行一项教科书练习，要求“使用布尔代数法则最小化以下布尔表达式，然后在不使用NOT门的情况下为其开发逻辑电路”。
表达式是X =（不是A）和（不是B或C）或不是（C或A）
首先，我试图最小化这个等式。 我使用左侧的分配法将（不是A）和（不是B或C）转换为（不是A而不是B）或（不是A和C）。
因此遵循这个定律，新的等式是（不是A而不是B）或（不是A和C）或（不是C而不是A）。
在（（不是A和C）OR（非C和非A））的右侧分组，表明还有另一个法则规定（AB + A（NOT B）= A）。
我在这里使用这个法律（称这个法律？）来简化整个表达式，简单地说就是NOT（A）。
所以新的等式是（不是A而不是B）或（不是A）。
我使用冗余定律，它表明（A + AB = A），将整个表达式改为NOT（A）。
在这个最小化之后，我已经成功地将整个方程最小化为X = NOT（A）。 真值表显示它们在功能上是等价的。
我的两个问题是1.我看到的地方？ 法律，我已经搜索了这个法律的名称，但一直找不到。 是否有法律名称（AB + A（非B）= A）？ 2.如果函数不是（A），我不确定如何在不使用NOT门的情况下设计逻辑电路？ 我在想，也许NAND门可以工作，但那些有逆变器。 如果它要求不使用NOT门，那么使用NAND门仍然有效吗？
感谢您的任何帮助。
I am working on a textbook exercise that asks to "Minimize the following boolean expression using boolean algebraic laws, and then develop a logic circuit for it WITHOUT using a NOT gate".
The expression is X= (NOT A) AND (NOT B OR C) OR NOT(C OR A)
First, I attempt to minimize this equation. I use distribute law of the left hand side to turn (NOT A) AND (NOT B OR C) to (NOT A AND NOT B) OR (NOT A AND C).
So following this law, the new equation is (NOT A AND NOT B) OR (NOT A AND C) OR (NOT C AND NOT A).
Grouping at the right hand side of ((NOT A AND C) OR (NOT C AND NOT A)), shows that there is another law that states (AB + A(NOT B) = A).
I use this LAW (Call this law ?) here to simplify the entire expression to simply NOT(A).
So the new equation is (NOT A AND NOT B) OR (NOT A).
I use the redundancy law, which states that (A + AB = A), to change the entire expression to simply NOT(A).
Following this minimization, I have successfully minimized the entire equation to X=NOT(A). Truth tables show they are functionally equivalent.
My two questions are 1. The area where I saw ? Law, I have searched for a name for this law but have not been able to find one. Is there a name for the law (AB + A(NOT B) = A)? 2. If the function is NOT(A), I am not sure how one could design a logic circuit without using a NOT gate? I was thinking that maybe a NAND gate could work, but those have inverters. If it asks to not use a NOT gate, is it still valid to use a NAND gate?
Thank you for any help.
最满意答案
AB + A(NOT B) = A没有名称，该等式只是分布定律 AB + A(NOT B) = A(B + NOT B)的结果， B + NOT B = TRUE的事实。
关于你对NAND的关注，是的，你需要使用它，因为没有办法从OR和AND得到NOT 。
There is no name for AB + A(NOT B) = A, the equation is just a consequence of the distribution law AB + A(NOT B) = A(B + NOT B) and the fact that B + NOT B = TRUE.
Regarding your concern about NAND, yes you need to used it because there is no way to get NOT from just OR and AND.
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