Chapter 3 - Review of Essential Terms and Concepts
What are the necessary steps one must take when designing a logic circuit from a description of the problem?
1. Defining problem: The designer should completely understand and analyze the problem. The description of the problem is thoroughly checked and requirements are analyzed. This step plays a very important role because without properly understanding the given problem, the circuit cannot be build efficiently. The fact is that no one can do anything if he does not know what to do. So, first we need to clearly define and understand the problem. 2. Finding number of inputs and outputs: After defining and understanding the problem clearly, the number of inputs that are to be given to the circuit and number of possible outputs that may be obtained from the circuit and number of possible outputs that may be obtained from the circuit should be analyze. The designer of circuit must consider this because the control lines creation is completely dependent on number of inputs and outputs which in turn plays an important role in operation of the circuit. 3. Constructing Truth Table: After analyzing the circuit problem and number of inputs and outputs, the truth table for the problem should be constructed and check the result obtained will satisfy the requirements of circuit or not. 4. Construction of Logic gates: Logic gates that appropriate for obtaining the relevant output must be found. The operations that are to be performed by the circuit and which logic gate will help to perform such operation should be chosen. The number of control lines and passing of inputs etc. need to be carefully designed. 5. Implementation: After analyzing all these factors and designing appropriate logic gates and truth table, the actual logic circuit is constructed and implemented in real time systems and check whether it is working properly or not.
In the context of digital circuits, what is feedback?
A concept used in circuits where the output of a circuit should fed back as input to the same circuit. The sequential circuits usually rely on feedback concept to implement chain and operate, in which the output is taken as input and processed and again the output produced is input to next state. This simple form of feedback is used for remembering the past state of circuit. The simple feedback circuit can be constructed using two NOT gates, which is not so useful in circuit operations but used to understand how feedback works. An SR flip-flop can also be constructed using two NOR gates. A feedback in digital circuit context can be used in any of the following ways: •It can be negative feedback also, which is used to control or regulate the opposing changes in output. •It is used as feedback signal which is used to convey the information led from input that affects the system. •It is used as feedback loop which is a closed path made and the path transmits the feedback from the origin to destination.
Name the four basic logic gates.
AND Gate OR Gate NOT Gate XOR Gate A Boolean expression is a combination of the Boolean variables and the operator.s The Boolean expression in combination with the result produced is termed as a Boolean function. AND, OR, and NOT are the three most commonly used operators. The Boolean expression is ultimately implemented by means of logical gates which are electronic devices. While the output of these devices gives us the desired result of the logical operations, it is the TRANSISTORS which comprise the hardware that realize these functions. Several transistors are put together and connected in a way to function as a compact, well-defined unit called a GATE to give the desired output for for a given set of inputs. While the basic operators AND, OR, and NOT each have their corresponding logical gates to implement them, there is yet another commonly used gate called the XOR gate. This gives the output as true when exactly one of the inputs is true. The four gates are diagrammatically represented as follows: (see attached image)
Which Boolean operation is referred to as a Boolean sum?
Boolean algebra employs the use of operations on Boolean variables to obtain desired results. A Boolean expression is a combination of the Boolean variables and the operators. The Boolean expression in combination with the result produced is termed as a Boolean Function. AND, OR, and NOT are the most commonly used operators. A plus "+" symbol is how the OR operator is represented. Suppose we have two Boolean variables A and B, the OR operation on these variables is represented as A + B. A truth table consists of all the possible input combinations and their output for a given Boolean function. The truth table for the OR operator is as follows. (see attached image) Hence, we can see from the truth table, that the output is actually a sum of the inputs. This is why the OR operator is known as the sum function.
Which Boolean operation is referred to as a Boolean product?
Boolean algebra employs the use of operations on Boolean variables to obtain desired results. A Boolean expression is a combination of the Boolean variables and the operators. The Boolean expression in combination with the result produced is termed as a Boolean function. AND, OR, and NOT are the three most commonly used operators. A dot "•" or simply no symbol at all is how the AND operator is represented. Suppose we have two Boolean variables A and B, the AND operation on these variables is represented as A•B or AB. A truth table consists of all the possible input combinations and their output for a given Boolean function. The truth table for the AND operator is as follows: (see attached image) Hence, we can see from the truth table that the output is actually a product of the inputs. This is why the AND operator is known as the product function.
Describe the basic construction of a digital logic chip.
Boolean algebra employs the use of operations on Boolean variables to obtain desired results. A Boolean expression is a combination of the Boolean variables and the operators. the Boolean expression in combination with the result produced is termed as a Boolean function. AND, OR and NOT are the three most commonly used operators. The Boolean expression is ultimately implemented by means of logical gates which are electronic devices. While the output of these devices gives us the desired result of the logical operations, it is the TRANSLATORS which comprise the hardware that realize these functions. a number of transistors are put together and connected in a particular way to function as a compact, well-defined unit called a gate to give the desired output for a given set of inputs. It is these gates that make up the entire circuit board of the computer systems. Wires, which serve as a signal pathways, connect the gates to facilitate the transfer of digital information that ultimately forms the core of data processing and the arithmetic calculations. A permanent etching is performed on the chip which is actually a flat base to hold a collection of the various electronic components such as capacitors, resistors and transistors etc. A plastic or ceramic container is the mounted on the chip. There are external chips presents on this container to which the connections from the chip are finally welded to form an integrated circuit.
Which filp-flop gives a true representation of computer memory?
D Flip Flop
What do we mean when we say that a sequential circuit is edge triggered rather than level triggered?
In level triggering the circuit becomes active when the clock pulse is at the particular level. We can say that level triggering is just like a baby when he is hungry have to feed them in whatever case. As long needed we have to keep care. Level trigger interrupt is an indication that device needs attention. While on the other hand edge triggering in the circuit becomes active while negative and positive edge of cycle. It is a type of event notification. When something happens it generates an active edge of the interrupt line. Hence in the sequential circuit, we cannot stop main task for a larger amount of time, that's why edge triggered is preferred over level trigger.
What is the difference between a gate and a circuit?
In order to implement a computer program, we would need a series of such logical gates connected in series or in parallel. Such a network of gates is called a DIGITAL CIRUIT. These circuits are able to perform complex arithmetic calculations through various combinations of connections among the gates.
Why is an understanding of Boolean algebra important to computer scientists?
In the case of objects which can only take one of two values: true or false, Boolean algebra can be used to manipulate them. Boolean algebra thus comes across as a very natural means of communication since holding definite values "on" or "off" are how computer switches work. These values are mostly realized baby means of low and high voltages. The low voltage generally denotes false while the high true. The importance of the binary algebra thus lies in its simplicity and its ability to convey information in a tacit yet precise manner.
What are the three methods we can use to express the logical behavior of Boolean functions?
It is not uncommon for a Boolean Expression not to be decomposable to a more compact and simple form. Boolean expressions can be simplified by certain rules which are known as identities. Each of these rules has an application to an expression in either the SUM form of the PRODUCT form. This flexibility of the rules is known as the duality principle. A Boolean function can also be represented as a Truth Table. The Truth Table is a means of sowing the output for every possible input to the function. Since all the possible input-output combinations are evaluated, it is sufficient to describe the function completely. Yet another way to represent the Boolean function is the logic diagram. This shows how the various logic gates such as AND, OR and NOT are connected and the various inputs passed on to them to give the desired result. This is thus analogical to the Boolean expression but is graphical rather than verbal in nature.
what is the Boolean duality principle?
It is not uncommon for a Boolean expression not to be decomposable to a more compact and simple form. Boolean expressions can be simplified by certain rules which are known as IDENTITIES. Each of these rules has an application to an expression in either the SUM form of the PRODUCT form. This flexibility of the rules is known as the duality principle.
Describe the operation of a ripple-carry adder. Why are ripple-carry adders not used in most computers today?
It is these gates that make up the entire circuit board of the computer systems. Wires, which serve as signal pathways, connect the gates to facilitate the transfer of digital information that ultimately forms the core of data processing and the arithmetic calculations. Such a set up is called a combinational circuit. And the basic example of such a circuit is the HALF ADDER. The HALF ADDER calculates the sum of two bits. It takes the two bits as input and outputs the result of the addition as two bits: sum and carry. The FULL ADDER is an extension of the half adder and it is capable of adding three bits: the two input bits as well as the carry from a previous addition. A set of such full adders connected in series could be used to add a pair of binary numbers of multiple lengths. Starting from the least Significant bit, we proceed to add each per of bits at the same level of significance. the result of each addition goes to the Sum bit, while the Carry (if any) gets passed on to the input carry of the next significant pair. The diagram from a ripple carry adder is shown as follows: (see image) Here, the pair of binary numbers is A0-An and B0-Bn. The carry results are passed on the the next pair after every bit addition, while the final result is represented by the sum i.e. S0-Sn together with the Final Carry Out. The reason this adder isn't widely implemented is that it is slow because the every carry needs to ripple through all the bit positions for the final bit pair to be evaluated. Parallel adders are thus preferred over the serial adders like the ripple-carry.
Why is it important for Boolean expressions to be minimized in the design of digital circuits?
The Boolean expression is ultimately implemented by means of logical gates which are electronic devices. If the expression evaluates the same set of inputs to give the desired result in a more concise manner, we would be saving not only on the hardware but also the time involved in procession the Boolean expression.
What is the relationship between transistors and gates?
The Boolean expression is ultimately implemented by means of logical gates which are electronic devices. While the output of these devices gives us the desired result of the logical operations, it is the TRANSISTORS which comprise the hardware that realize these functions. A number of transistors are put together and connected in a particular way function as a compact, well-defined unit called a GATE to give the desired output for a given set of inputs.
What kind of circuit selects binary information form on of many input lines and directs it to a single output line?
The Boolean expression is ultimately implemented by means of logical gates which are electronic devices. While the output of these devices gives us the desired result of the logical operations, it is the TRANSISTORS which comprise the hardware that realize these functions. A number of transistors are put together and connected in a particular way to function as a compact, well-defined unit called a GATE to give the desired output fro a given set of inputs. In some cases, however, we would need to select a particular input from a set of inputs. The output thus would need to be dependent on only one one from a range of inputs. Selection variables are used to select a particular input line. This is basically done by cutting out the others. One application of multiplexers is for timesharing, where multiple users share the computer on a timeslot allocation basis.
What does an algorithmic state machine offer that is not provided by either a Moore or a Mealy machine?
The dimension provided by the timer, along with the numerous signals that define a state is hard to capture in the Moore or Mealy models. (microwave) An algorithmic state machine is directed at expressing the algorithms that advance an FSM from one stat to another. An ASM consists of blocks that contain a state box, a label, and optionally conjoint and output boxes. And has one entry point and at least one exit point. Moore type outputs are indicated inside the state block and Mealy type outputs are indicated in the oval input box.
What is the difference between a half-adder and a full-adder?
The half adder calculates the sum of two bits. It takes the two bits as input and outputs the result of the addition as two bits: sum and carry. The full adder is an extension of the half adder and it is capable of adding three bits: the two input bits as well as the carry from a previous addition. A set of such full adders connected in series could be used to add a pair of binary numbers of multiple lengths. Starting from the Least Significant bit, we proceed to add each pair of bits at the same level of significance. The result of each addition goes to the Sum bit, while the Carry (if any) gets passed on to the input carry of the next significant pair.
What do we call a circuit that takes several inputs and their respective values to select one specific output line? Name one important application for these devices.
The implementation of the Boolean expression is ultimately done with the help of logical gates which are electronic devices. While the output of these devices gives us the desired result of the logical operations, it is the transistors which comprise the hardware that realize these functions. A gate in which number of transistors are put together and connected in a particular way to function as a compact, well-defined unit to give the desired output for a given set of inputs. In some cases, however, there is more than just a binary output. It involves a selection of one from a possible outputs set. The number of outputs is mainly in powers of 2 and hence is in the form 2^n. The number of input lines is n. While selecting a particular function from a multi-function device is one of the applications of the decoder. The user inputs, the desired function to be performed, by means of a code and the device carries out that specific function based on the user command.
Why are JK flip-flops often preferred to SR flip-flops?
The main difference between a JK flip-flop and an SR flip-flop is that in the JK flip-flop, both inputs can be HIGH. When both the J and K inputs are HIGH, the Q output is toggled, which means that the output alternates between HIGH and LOW. Thereby the invalid condition which occurs in the SR flip-flop is eliminated.
How are sequential circuits different from combinational circuits?
There are two broad categories of circuits: COMBINATIONAL and SEQUENTIAL Basic boolean inputs, operators and outputs are build with the help of COMBINATIONAL logic. A combinational circuit is generally recognized by the fact that the output is based entirely on the inputs fed into the circuit. Not only do the inputs totally determine the outputs, but they also uniquely identify them. A number of possible outputs could be associated with a given circuit. Boolean functions are each represented by a particular output. Unlike a combinational circuit, the output of a SEQUENTIAL circuit is based not only on the current given inputs but also on past inputs. A storage capability is thus needed to remember previous inputs to the circuit. FLIP-FLOP is the name associated with such a storage element. Previous inputs to this storage element all have an effect on the current state of the flip-flop. Flip-flops interconnected to form sequential circuits in a method analogous to how gates combine to form combinational circuits.
What is the basic element of a sequential circuit?
There are two broad categories of circuits: combinational and sequential •Basic Boolean inputs, operators, and outputs are built with the help of combinational logic. A combinational circuit is generally recognized by the fact that the output is based entirely on the inputs fed into the circuit. Not only do the inputs totally determine the outputs, but they also uniquely identify them A number of possible outputs could be associated with a given circuit. Boolean functions are each represented by a particular output. •Unlike a combinational circuit, the output of a sequential circuit is based not only on the current given inputs but also on past inputs, A storage capability is thus needed to remember previous inputs to the circuit. Flip-flop is the name associated with such a storage element. Previous inputs to this storage element all have an effect on the current state of the flip-flop. Flip-flops interconnect to form sequential circuits in a method analogous to how gates combine to form combinational circuits.
What are the two universal gates described in the chapter? Why are these universal gates important?
To obtain desired results, Boolean algebra employs the use of operations on Boolean variables. The Boolean variables combined with the operators is said to be the Boolean expression. The Boolean function is said to be the combination of a Boolean Expression with the result produced. The three most commonly used operators are AND, OR and NOT. It is very common that a Boolean expression not to be decomposable to a more compact and simple form. Certain rules can simplify the Boolean expression in which they are said to be the identities. An application to an expression for each rule is either the SUM form of the PRODUCT form. These rules flexibility is said to be known as the PRINCIPLE OF DUALITY. Gates such as the NAND and NOR which is basically AND *with line over* (the Complementary result of AND gate) and OR *with line over* (the Complementary result of OR gate) are used to realize this. This is due to fact that ANY circuit can be built using only one of these two types of gates. Any single type of these gates can be used to make the primitive elements AND, OR and NOT GATES. These are the primary reasons which declare these two gates are said to be the universal gates. There are two primary advantages to using the same type of gate to build a circuit and it is as follows: •Since the lesser number of gates gets involves, it is cheaper. •In case of complex circuitry, the interconnection would also be a lot simpler.
How is a JK flip-flop related to an SR flip-flop?
•The JK flip-flop is fundamentally an improved version of gated SR flip-flop with additional clock input circuit. In the SR flip-flop, when the clock is triggered both the inputs should not be "HIGH". •If there is an occurrence of this state, then it is considered as an invalid state and the resultant output is not predictable. •The key difference between a JK flip-flop and an SR flip-flop is that in the former, both the input can be "HIGH" because of the presence of additional clock input circuit. •While both J and K inputs are "HIGH", the Q resultant output is toggled meaning that the resultant output can alternate between "LOW" and "HIGH". •Thus the invalid state or condition that occurs in the SR flip-flop can be eliminated. •Hence this is how JK flip-flop is related to the SR flip-flop.
