Here, we provided to Best Digital Logic Hand Written Note. Digital, or boolean, logic is the fundamental concept underpinning all modern computer systems. Put simply, it’s the system of rules that allow us to make extremely complicated decisions based on relatively simple “yes/no” questions. Free download PDF Best Digital Logic Hand Written Note.
Digital logic circuits can be broken down into two subcategories- combinational and sequential. Combinational logic changes “instantly”- the output of the circuit responds as soon as the input changes (with some delay, of course, since the propagation of the signal through the circuit elements takes a little time). Sequential circuits have a clock signal, and changes propagate through stages of the circuit on edges of the clock.
Typically, a sequential circuit will be built up of blocks of combinational logic separated by memory elements that are activated by a clock signal. Free download PDF Best Digital Logic Hand Written Note.
Digital logic is important in programming, as well. Understanding digital logic makes complex decision making possible in programs.
There are also some subtleties in programming that are important to understand; we’ll get into that once we’ve covered the basics.
- AND gate – output is 1 if BOTH inputs are 1
- OR gate – output is 1 if AT LEAST one input is 1
- XOR gate – output is 1 if ONLY one input is 1
- NAND gate – output is 1 if AT LEAST one input is 0
- NOR gate – output is 1 if BOTH inputs are 0
There is a sixth element in digital logic, the inverter (sometimes called a NOT gate). Inverters aren’t truly gates, as they do not make any decisions. The output of an inverter is a 1 if the input is a 0, and vise versa. Free download PDF Best Digital Logic Hand Written Note.
BOOK NAME – BEST DIGITAL LOGIC HAND WRITTEN NOTE
SIZE – 873.44KB
PAGES – 10
Written Boolean Logic:
It is, of course, useful to be able to write in a simple mathematical format an equation representing a logical operation. To that end, there are mathematical symbols for the unique operations: AND, OR, XOR, and NOT. Free download PDF Best Digital Logic Hand Written Note.
- A AND B should be written as AB (or sometimes A • B)
- A OR B should be written as A + B
- An XOR B should be written as A ⊕ B
- NOT A should be written as A’ or A
Combinational logic is great, but without adding sequential circuitry, modern computing would not be possible.
Sequential circuitry is what adds memory to our logical systems. As mentioned earlier, combinational logic produces results after a delay. That delay varies according to lots and lots of things: the manufacturing process of the parts involved, the temperature of the silicon, the complexity of the circuit. If the output of a circuit is dependant upon results from two other combinational circuits and the results arrive at different times (which they will, in the real world), a combinational circuit will “glitch” briefly, outputting a result which may not be consistent with the desired operation. Free download PDF Best Digital Logic Hand Written Note.
A sequential circuit, however, only samples and propagates the output at specific times. If the input changes between those times, it is ignored. The sampling time is usually synchronized across the entire circuit and is referred to as the “clock”. When a computer’s “speed” is cited, this is the value in question. It is possible to design “asynchronous” sequential circuits, which do not rely on a synchronized global clock. However, those systems pose great difficulties, and we won’t be discussing them here.
As a side note, any section of digital logic will have two characteristic delay values: the minimum delay time and the maximum delay time. If the circuit fails the minimum delay time (i.e., is faster than it should be), the circuit will fail, irreparably so. If that circuit is part of a larger device, like a computer CPU, the entire device is garbage and cannot be used.
If the maximum delay time fails (i.e., the circuit is slower than it should be), the clock speed can be reduced to accommodate the slowest circuit in the system. Maximum delay times tend to go up as the silicon forming a circuit warms up, which is why computers become unstable when they overheat or as the clock speed is increased (as is the case with overclocking).
Application Of Logic Gates:
Logic gates have a lot of applications but they are mainly based upon their mode of operations or their truth table. Basic logic gates are often found in circuits such as safety thermostat, push-button lock, automatic watering system, light-activated burglar alarm, and many other electronic devices. Free download PDF Best Digital Logic Hand Written Note.
One of the primary benefits is that basic logic gates can be used in a mixture of different combinations if the operations are advanced. Besides, there is no limit to the number of gates that can be used in a single device. However, it can be restricted due to the given physical space in the device. In digital integrated circuits (ICs) we will find an array of the logic gate area unit.
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