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# Tag Info

## Hot answers tagged boolean-algebra

49 votes

### How did people realize they could do logic with electronics?

From the Wikipedia article, Boolean algebra: In the 1930s, while studying switching circuits, Claude Shannon observed that one could also apply the rules of Boole's algebra in this setting, and he ...
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43 votes

### Why does F + F' = 1?

The point is, it really doesn't matter what the function $f()$ actually is. The key fact is that its output is a single binary value. It is a fundamental fact in Boolean algebra that the complement ...
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34 votes

### How did people realize they could do logic with electronics?

As with so many other important developments in logic and computer science, it was almost certainly the mathematician and philosopher Charles Sanders Peirce, whose work predated Shannon's by decades: ...
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31 votes
Accepted

### What will happen if the output from a NOT-gate injected- BACK to its OWN input?

What happens is usually cases 3. or 5. You have not defined case 5 :-) The joined input-output will sit at some voltage near the middle of the supply. 74HC14: When a Schmitt triggered gate is ...
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25 votes
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### Digital Logic circuit - exam question

I wrote an algorithm in C# that tries every possible combination of those Nor 3->1 Xor 2->1 ...
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23 votes

### What will happen if the output from a NOT-gate injected- BACK to its OWN input?

what you are describing is called a Ring oscillator Your output will oscilate with a certain frequency depending of the gate delay of your NOT gate. A perfect NOT Gate would oscillate with an ...
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14 votes
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### Build circuit from a formula

I want to start out by showing you something that in this particular case isn't much of a difference, but is an allowed technique just the same. I moved rows 2 and 3 from your original map on the ...
• 78.4k
14 votes

### Why does F + F' = 1?

All previous answers are correct, and very much in depth. But a simpler way to approach this might be to remember that in boolean algebra, all values must be either 0 or 1. So... either F is 1, ...
• 595
13 votes

### What will happen if the output from a NOT-gate injected- BACK to its OWN input?

Looking at the transistor schematic it can be seen that the resulting circuit consists of two transistors that have their gates connected to their drains. This so called "diode-connected" transistor ...
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13 votes

### My Professor and I are debating about absorption law

I like the OP's insight better but here is a step by step solution. ...
• 1,149
11 votes

### Why does F + F' = 1?

My answer is similar to the one of Dave Tweed, meaning that I put it on a more formal level. I obviously answered later, but I decided to nevertheless post it since someone may find this approach ...
• 3,395
11 votes

### Why does F + F' = 1?

All good answers that provide the necessary justification in one way or the other. Since it is a tautology, it's hard to create a proof that doesn't just result in "it is what it is!". Perhaps this ...
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9 votes
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6 votes

### Meaning of logic operation " a' "

$'$ is complement operator in that context. $A'$ is also equivalent to $\overline A$. It signifies a negation on boolean variable $A$, ie., $\text{not } A$. So the expression in your ...
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6 votes
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### Create a logic circuit only using AND & OR gates

We know, that the gates AND and OR do not form a functionally complete set. It is true even if we add constants 0 and 1 to it. ...
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6 votes
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### Intuition behind two laws of Boolean Algebra

X AND X is X and is the same as X AND 1 (because that will always take the value of X). Why ...
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5 votes

### How did people realize they could do logic with electronics?

Strowger's 1889 automatic telephone exchange was certainly a practical and real world use of digital logic via electromechanical means. Solving other pulse/state logic problems with relays and other ...
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5 votes
Accepted

### Is there an intuitive reason for why NAND gate is a universal gate?

Now I know the maths and logic to figure out that every boolean function can be expressed using only AND and OR gates Untrue. You also need inverters. every boolean function can be expressed ...
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5 votes

### Simplify the boolean function $$Z=A\bar B \bar{C_i} + \bar A B \bar{C_i} + \bar A\bar B {C_i} + A B {C_i}$$

Observe that \begin{align}\overline{\overline{A} \cdot\overline{B} + A\cdot B} = \overline{(\overline{A}\cdot\overline{B})}\cdot\overline{(A \cdot B)} = (A + B)\cdot(\overline{A}+\overline{B}) = A \...
• 2,331

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