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 ...
The Photon's user avatar
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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 ...
Dave Tweed's user avatar
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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: ...
Mark Dominus's user avatar
31 votes
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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 ...
Russell McMahon's user avatar
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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 ...
Ido Kessler's user avatar
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 ...
KarlKarlsom's user avatar
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14 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 ...
Mario's user avatar
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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 ...
jonk's user avatar
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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, ...
Opifex's user avatar
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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. ...
Syed's user avatar
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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 ...
Daniele Tampieri's user avatar
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 ...
Heath Raftery's user avatar
10 votes

Determining minimum number of NAND/NOR gates required to realize a Boolean expression

You can only find the minimum number of gates in a multi-level network by solving an integer programming problem [or equivalents, see below]. This problem is NP-complete, so only practical to solve up ...
Dolphin 613 Motorboat's user avatar
9 votes
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How do you implement the following function using nothing but 2:1 MUX?

It's not too complex, I think, assuming you worked out the equation you wanted correctly (I'll assume you did okay there.) Start by looking at the equation for a 2-in MUX: $$ \begin{align*} M_2(A,B,S)...
jonk's user avatar
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9 votes

How did people realize they could do logic with electronics?

As far as "eureka" moments go, I think the application of Boolean logic to electronics became inevitable the moment Boolean Algebra was formalized by George Boole in ...
MaxPRafferty's user avatar
8 votes

How Would a CPU Improve if its Logic Circuits were Reduced?

I worked for a decade at a startup doing computerised logic improvement for chip designers; we were eventually bought by Cadence. We had, among a whole bunch of other tools, a heuristic logic ...
pjc50's user avatar
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8 votes
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What is this trapezoidal logic gate?

It's a multiplexer. When the input on the side has a specific value, the input corresponding to that value is propagated to the output. It's not a single gate per se but rather is composed of several ...
Ignacio Vazquez-Abrams's user avatar
8 votes

Digital Logic circuit - exam question

This is a non-answer, to discard the most obvious solution. I will number bits by its weight: \$ b_1 \$, \$ b_2 \$, \$ b_4 \$ and \$ b_8 \$. As bits \$ b_2 \$ and \$ b_4 \$ are equal in all the ...
pasaba por aqui's user avatar
8 votes

Why does F + F' = 1?

F + F' = 1 means that you have to show that no matter the state of the 4 inputs, OR'ing the result of those 2 always result in 1, A few minutes in excel shows it is indeed the case. You can use "...
Reroute's user avatar
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8 votes
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Electrical counterpart: Logical not

if you need just signal, you can use also transistor - less power consumption, can work directly with IC: https://www.electronics-tutorials.ws/logic/logic_4.html
petr's user avatar
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7 votes

How to build a 3-input NAND gate from 2-input NAND gates or a 3-input NOR gate from 2-input NOR gate?

An alternate approach is given. simulate this circuit – Schematic created using CircuitLab The schematic represents the function: $$Y = \overline{ABC} = \overline{\overline{\overline{AB}} C}$$
nidhin's user avatar
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7 votes

How did people realize they could do logic with electronics?

This excellent Atlantic article answers your question at length. Here's the closest thing to a Eureka moment: Today, Boole’s name is well known to computer scientists (many programming languages ...
Biro Cash's user avatar
7 votes
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how is this conversion possible?

I am confused why NOT1 was replaced with NAND4? First, it sould be clear why it was legitimate to do so - a NAND gate with the inputs joined is just an inverter. To understand the motivation why it ...
Chris Stratton's user avatar
6 votes
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Are digital Electronics and Logic Unified?

Knowledge of Digital Logic underpins knowledge of Digital Electronics, but in practice you have to understand more than just the basics. the reference to "our logic works on falling edge," is almost ...
Jotorious's user avatar
  • 659
6 votes

What is this trapezoidal logic gate?

I's a multiplexer. Logically it is the same as the following circuit: simulate this circuit – Schematic created using CircuitLab
ratchet freak's user avatar
6 votes

What heuristics are there (if any) to know how close a circuit is to a function?

You could base your "cost function" on DNF fault classes. For a start, you could consider the following set ENF: expression negation fault (a -> !a) TOF: term omission fault (a -> a | b) TIF: term ...
Dmitry Grigoryev's user avatar
6 votes
Accepted

How come (x*y)+(x*z')+(y*z) = (x*z')+(y*z)?

You have $$\bar{x}yz + x\bar{y}\bar{z} + xy\bar{z} + xyz = (x + \bar{x})yz + (y + \bar{y})x\bar{z} = yz + x\bar{z}.$$ Alternatively $$xy + yz + x\bar{z} = xy(z + \bar{z}) + yz + x\bar{z} = (1 + x)...
user110971's user avatar
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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 ...
Meenie Leis's user avatar
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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. ...
Eugene Sh.'s user avatar
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 ...
Arsenal's user avatar
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