Home » Books » Philosophy » Introduction to Logic. Genres: Philosophy. This textbook was written with the fully onlinc student and the independent learner in mind. Not that this book is unsuitable for the face-to-face class.
The fact that this book was written with the online learner in mind means less content will need to be explained in the classroom, leaving more time for discussion and practice. Logical theory unfolds historically, as a story starting in ancient Athens and reaching undreamed of heights in the late twentieth century. I hope you will agree that historical context not only adds personality to a course that can be pretty dry if you let it be, it also makes the logic course more interesting.
Many of the great logicians of history were interesting characters, and the conceptual problems they sought to solve were serious ones. Some of the material in this book appeared in an earlier textbook that I wrote, Tlte Many Worlds of Logic, first published in Oxford University Press published the second edition of that book. This new book covers everything treated in Many Worlds and more.
The difference between my earlier book and this book stems from two intervening experiences. It was my experiences as an online logic teacher that inspired me to begin this textbook. Most of us move through the subject in a roughly historical order anyway.
After laying down fundamental concepts, we often progress from Aristotelian to truth-functional to predicate logic, perhaps visiting informal and inductive logic along the way.
With this new text I plan to teach logic as a fascinating, human story unfolding over time, as well as a body of important technical information with applications to every area of human thought. The two approaches-the historical and the technical-do not have to be kept separate. They are intertwined in this book. Every quarter, one or two students always ask about advanced logic.
I am sure you have been asked the same questions. With this new textbook I will no longer have to send the student off to a university library. What difference does it all make anyway? I am sure you have been asked these or similar questions, perhaps even in front of the class. In this tutorial, we will have a brief introduction to Logic Gates.
Logic gates are the heart of digital electronics. A gate is an electronic device which is used to compute a function on a two valued signal. Logic gates are the basic building block of digital circuits.
Basically, all logic gates have one output and two inputs. Some logic gates like NOT gate or Inverter has only one input and one output. The inputs of the logic gates are designed to receive only binary data only low 0 or high 1 by receiving the voltage input. The low logic level represents Zero volts and high logic level represents 3 or 5 volts positive supply voltage.
We can connect any number of logic gates to design a required digital circuit. Practically, we implement the large number of logic gates in ICs, by which we can save the physical space occupied by the large number of logic gates.
We can also perform complicated operations at high speeds by using integrated circuits IC. By combining logic gates, we can design many specific circuits like flip flops, latches, multiplexers, shift registers etc. A logic level is defined as a specific state or voltage of a signal. We know that 0 and 1 are the two states of logic gates. In digital electronics, these binary logic levels play a crucial role in data storage, data transfer.
As we said earlier, the logic levels are introduced to the logic gate by the supply voltage. If the supply voltage to the logic gate is 0 volts, it refers to Low logic level or OFF state. Similarly, if the supply voltage to the logic gate is 5 volts or 3.
We see the active high input and active low input pins in ICs and micro controllers. Do you know what they really mean? They just describe us how the pin is getting activated. This means the Active low pin must be connected to low logic level or Ground.
In the same way, the Active high pin must be connected to high logic level or to 5 volts or 3. When we see the enable pin CE in a shift register IC, without any line bar on it, we connect it to active low input i. TTL logic level is the standard logic level for majority of the logic devices. Transistors are electrically controlled switches. The voltage levels of logic families are. If we observe the TTL logic levels, we can observe that the minimum high voltage level for output is 2. This means, when the device is driving HIGH, the voltage should be at least 2.
Similarly, the minimum high voltage level for input is 2 volts. So the voltages greater than 2 volts will considered as logic 1, to a TTL device. The voltages between 0. In the same way, the maximum LOW voltage level for output is 0. This means, when the device is driving HIGH, the voltage should be less than 0. Similarly, the maximum low voltage level for input is 0.
So the voltages less than 0 volts will consider as logic 0, to a TTL device. So when the logic device is supplied with voltages between 0. CMOS logic devices are also known as 3. This is an advanced technology that will run the devices on low power supply 3. For example, the minimum value for a high logic level 1 of a CMOS device is 2. Because many of the will permanently cause the chip damage when we supply voltages above 3.
We can use a voltage divider circuit or logic level shifters to control the 5 V voltage signals. The noise margin of a logic level is defined as the voltage gap between the maximum low voltage of high input VIL max and maximum voltage of the low input VIL min of a logic gate. The noise margin is also defined as the amount by which the voltage signal exceeds the threshold level for the exact high or exact low.
When a logic circuit is altering between 0 volts and 1. And any voltage above 1 volt is considered as HIGH i. CMOS logic devices have higher noise level or noise margin than TTL logic devices because their minimum output voltage for high logic VOH min is closer to the supply voltage and maximum output voltage for low logic VOL max is nearly 0.
So the noise level is the maximum amount of noise that a logic circuit can withstand. If we apply a voltage of certain the noise level, we do not certainly know whether the circuit will respond or not. Noise level is the unwanted voltage level, caused by external interference such as supply voltage fluctuations and other conductors in circuit.
For TTL devices the tolerance range of output voltages is higher than that of input voltages. Diodes can act like switches, so these are used in digital logic operations and switching. For low and high impedance states a diode will work in forward bias and reverse bias. The diode will conduct only in one direction Forward bias and it remains closed in reverse bias condition.
So it behaves like a switch. The simple OR gate designed by two diodes is shown in the below figure. Inputs are given to this circuit by the two diodes.
Thus the output is logic HIGH i. The truth table and logic diagram and circuit diagram for the logical OR gate is shown below. The simple AND gate designed by two diodes is shown in the below figure.
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