Chapter 3
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.
An equally important operation that all computers use frequently is decoding binary information from a set of nn inputs to a maximum of 2^n2n outputs. A decoder uses the inputs and their respective values to select one specific output line. "Selecting an output line" simply means that one unique output line is asserted, or set to 1, whereas the other output lines are set to 0. Decoders are normally defined by the number of inputs and the number of outputs. For example, a decoder that has 3 inputs and 8 outputs is called a 3-to-8 decoder.
What is the Boolean duality principle?
As in high school algebra, the expressions can be simplified, Boolean expressions can also be simplified, but we need new identities, or laws, that apply to Boolean algebra instead of regular algebra. These identities are called duality principle because it consists of the Sum (or) and Product (and) forms.
Why are JK flip-flops often preferred to SR flip-flops?
Input (S, R) = (1,1) is not allowed in SR flip-flop, as the result is undefined. By adding some conditioning logic to SR flip-flop, the illegal input (1,1) can be solved, which then makes SR flip-flop to be JK flip-flop (kind of update). Keeping it stable. Because of this feature of JK circuits, it is often preferred to SR circuits.
What is the difference between a gate and a circuit?
Logic gates are used to represent simple Boolean operators such as ANDAND, OROR, and NOTNOT. More complex Boolean expressions can be represented as combinations of these gates, resulting in a logic diagram that describes the entire expression. This logic diagram represents the physical implantation of the given expression or the actual digital circuit.
What do we mean when we say that a sequential circuit is edge-triggered rather than level-triggered?
Most sequential circuits are edge triggered, which means the circuit is allowed to change its state (active or passive) on either the rising or falling edge of the clock signal. The oppose of the term edge triggered - a level-triggered circuit is allowed to change its state (active or passive) whenever the clock signal is either high or low.
What kind of circuit selects binary information from one of many input lines and directs it to a single output line?
Multiplexer circuit selects binary information from one of many input lines and directs it to a single output line. The selection of a particular input line is controlled by a set of selection variables or control lines. At any given time, only one input (the one selected) is routed through the circuit to the output line. All other inputs are "cut off." If the values on the control lines change, the input is actually routed through changes as well.
What are the two universal gates described in this chapter? Why are these universal gates important?
NAND and NOR gates are commonly referred to as universal gates. These gates are important to use because: these gates are cheaper to build than the other gates; complex integrated circuits (which are discussed in the following sections) are often much easier to build using the same building block (i.e., several NAND gates) rather than a collection of the basic building blocks (i.e., a combination of AND, OR, and NOT gates).
Which Boolean operation is referred to as a Boolean sum?
The Boolean operator OROR is typically represented by a plus sign. Therefore, the expression x + yx+y is read "xx oror yy". The result of x + yx+y is 00 only when both of its input values are 00. The expression x + yx+y is often referred to as a Boolean sum. The Truth Table of the logical operator OROR:
How is a JK flip-flop related to an SR flip-flop?
The JK flip-flop circuit is basically the same as the SR flip-flop. The main difference is that the JK circuit negates the state if the input set is (J, K) = (1,1).
What is the relationship between transistors and gates?
The actual physical components, or digital circuits, such as those that perform arithmetic operations or make choices in a computer, are constructed from a number of primitive elements called gates. To physically implement each gate requires from one to six or more transistors, depending on the technology being used. To summarize, the basic physical component of a computer is the transistor; the basic logic element is the gate.
Which Boolean operation is referred to as a Boolean product?
The logical operator ANDAND is typically represented by either a dot or no symbol at all. For example, the Boolean expression xyxy is equivalent to the expression x º yxºy and is read "x and y." The expression xyxy is often referred to as a Boolean product. The Truth Table of the logical operator ANDAND:
Why is it important for Boolean expressions to be minimized in the design of digital circuits?
The minimized Boolean expression uses less time and hardware than the original one (not a simplified one). Thus minimizing the expressions are important in the design of digital circuits.
What is the basic element of a sequential circuit?
Therefore, the output depends on past inputs. To remember previous inputs, sequential circuits must have some sort of storage element - called a flip-flop. The state of this flip-flop is a function of the previous inputs to the circuit. Therefore, pending output depends on both the current inputs and the current state of the circuit. Flip-flop is the basic element of sequential circuits. In the same way that combinational circuits are generalizations of gates, sequential circuits are generalizations of flip-flops.
In the context of digital circuits, what is feedback?
To "remember" a past state, sequential circuits rely on a concept called feedback. This simply means the output of a circuit is fed back as an input to the same circuit. A very simple feedback circuit uses two NOTNOT gates, as shown in the figure below. In this figure, if Q is 0, it will always be 0 (0->1->0). If Q is 1, it will always be 1 (1->0->1). This is not a very interesting or useful circuit, but it allows to see how feedback works.
Describe the basic construction of a digital logic chip.
Typically, gates are not sold individually; they are sold in units called integrated circuits (ICs). A chip (a silicon semiconductor crystal) is a small electronic device consisting of the necessary electronic components (transistors, resistors, and capacitors) to implement various gates. Digital logic chips are combined to give us useful circuits. These logic circuits can be categorized as either combinational logic or sequential logic.
Describe the operation of a ripple-carry adder. Why are ripple-carry adders not used in most computers today?
adding two set of bits, carrying any remainder of bits to another adder adder is very slow, it is not normally implemented.
How are sequential circuits different from combinational circuits?
Combinational is based entirely on inputs while sequential takes into account the memory of previous inputs
Which flip-flop gives a true representation of computer memory?
D (data) flip-flop is another variant of SR flip-flop circuits. D (data) flip-flop circuit is a true representation of physical computer memory. QQ is the current state of the device. This sequential circuit (D (data) flip-flop) stores one bit of information. If a 1 is asserted on the input line D, and the clock is pulsed, the output line Q becomes a 1. If a 0 is asserted on the input line and the clock is pulsed, the output becomes 0. So, an output value of 1 means the circuit is currently "storing" a value of 1.
Name 4 basic logic gates
AND, OR, NOT, XOR
Why is an understanding of Boolean algebra important to computer scientists?
Boolean algebra is an algebra for the manipulation of objects that can take on only two values, typically true and false, although it can be any pair of values. Because computers are built as collections of switches that are either "on" or "off", Boolean algebra is a natural way to represent digital information. In reality, digital circuits use low and high voltages, but for our level of understanding, 0 and 1 will suffice. It is common to interpret the digital value 0 as false and the digital value 1 as true. Boolean algebra's application in the design of modern computing systems is significant. Understanding how Boolean logic affects the design of various computer system components will allow computer scientists to use, from a programming perspective, any computer system more effectively.
