Digital Logic

This chapter builds upon the introductory topics presented in Chapter 1, Introducing Computer Architecture, and provides a firm understanding of the digital building blocks used in the design of modern processors and other sophisticated electronic circuits. We begin with a discussion of basic electrical circuit elements. Next, we introduce transistors and examine their use as switching components in simple logic gates. We then construct latches, flip-flops, and ring counters from logic gates. More complex processor components, including registers and adders, are developed by combining the devices introduced earlier. The concept of sequential logic, which means logic that contains state information that varies over time, is developed. The chapter ends with an introduction to hardware description languages, which represent the design method of choice for complex digital devices.

The following topics will be covered in this chapter:

• Electrical circuits
...

Technical requirements

Files for this chapter, including answers to the exercises, are available at https://github.com/PacktPublishing/Modern-Computer-Architecture-and-Organization-Second-Edition.

Electrical circuits

We begin this chapter with a brief review of the properties of electrical circuits.

Conductive materials, such as copper, exhibit the ability to easily produce an electric current in the presence of an electric field. Nonconductive materials, for example, glass, rubber, and polyvinyl chloride (PVC), inhibit the flow of electricity so thoroughly that they are used as insulators to protect electrical conductors against short circuits. In metals, electrical current consists of electrons in motion. Materials that permit some electrical current to flow, while predictably restricting the amount allowed to flow, are used in the construction of resistors.

The relationship between electrical current, voltage, and resistance in a circuit is analogous to the relationship between flow rate, pressure, and flow restriction in a hydraulic system. Consider a kitchen water tap: pressure in the pipe leading to the tap forces water to flow when the valve is opened. If the...

The transistor

A transistor is a semiconductor device that, for the purpose of this discussion, functions as a digital switch. A semiconductor is a material that exhibits properties between those of good conductors (like copper wire) and good insulators (like glass or plastic). In a suitable circuit configuration, the conductivity of a semiconductor device can be varied by a control input. A transistor used in this manner becomes a digital switching element.

The transistor switching operation is electrically equivalent to changing between very high and very low resistance based on the state of an input signal. One important feature of switching transistors is that the switching input does not need to be very strong.

This means that a very small current at the switching input can turn on and turn off a much larger current passing through the transistor. A single transistor’s output current can drive many other transistor inputs. This characteristic is vital to the development...

Logic gates

Figure 2.3 is a schematic diagram of a transistor NOT gate. This circuit is powered by a 5 V supply. The input signal might come from a pushbutton circuit that produces 0 V when the button is not pressed and 5 V when it is pressed. R1 limits the current flowing from the input terminal to the transistor base terminal when the input is high (near 5 V). In a typical circuit, R1 has a value of about 1,000 ohms. R2 might have a value of 5,000 ohms. R2 limits the current flowing from the collector to the emitter when the transistor is switched on:

Figure 2.3: Transistor NOT gate

The input terminal accepts voltage inputs over the range 0 to 5 V, but since we are interested in digital circuit operation, we are only interested in signals that are either near 0 V (low) or near 5 V (high). We will assume that all voltage levels between the low and high states are transient during near-instantaneous transitions between the low and high states.

A typical NPN transistor...

Latches

Combinational logic does not directly permit the storage of data as is needed for digital functions such as processor registers. Logic gates can be used to create data storage elements by using feedback from a gate output to the input of a gate preceding that point in the signal chain.

A latch is a single-bit memory device constructed from logic gates. Figure 2.10 shows a simple type of latch called the Set-Reset, or SR, latch. The feature that provides memory in this circuit is the feedback from the output of the AND gate to the input of the OR gate:

Figure 2.10: SR latch circuit

Based on the inputs S and R, the circuit can either set the output Q to high, reset Q to low, or cause the output Q to be held at its last value. In the hold state, both S and R are low, and the state of the output Q is retained. Pulsing S high (going from low to high then back to low) causes the output Q to go high and remain at that level. Pulsing R high causes Q to go low and...

Flip-flops

A device that changes its output state only when a clock signal makes a specified transition (either low to high or high to low) is referred to as an edge-sensitive device. Flip-flops are similar to latches, with the key difference being that the output of a flip-flop changes in response to a clock edge rather than responding continuously to its input signal while enabled.

The positive edge-triggered D flip-flop is a popular digital circuit component used in a wide variety of applications. The D flip-flop typically includes set and reset input signals that perform the same functions as in the SR latch. This flip-flop has a D input that functions just like the D input of the gated D latch. Instead of an enable input, the D flip-flop has a clock input that triggers the transfer of the D input to the Q output and, with inversion, to the output on the clock’s rising edge. Other than within a very narrow time window surrounding the rising edge of the clock signal...

Registers

Processor registers temporarily store data values and serve as input to and output from a variety of instruction operations, including data movement to and from memory, arithmetic, and bit manipulation. Most general-purpose processors include instructions for shifting binary values stored in registers to the left or right and for performing rotation operations in which data bits shifted out one end of the register are inserted at the opposite end. The rotation operation is similar to the ring counter, except the bits in a rotation can hold arbitrary values, while a ring counter typically transfers a single 1 bit through the sequence of locations. Circuits performing these functions are constructed from the low-level gates and flip-flops presented earlier in this chapter.

Registers within a processor are usually written and read in parallel, meaning all the bits are written or read on individual signal lines simultaneously under the control of a common clock edge. The...

Adders

General-purpose processors usually support the addition operation for performing calculations on data values and, separately, to manage the instruction pointer. Following the execution of each instruction, the instruction pointer increments to the next instruction location.

When the processor supports multi-word instructions, the updated instruction pointer must be set to its current value plus the number of words in the just-completed instruction.

A simple adder circuit adds two data bits plus an incoming carry and produces a 1-bit sum and a carry output. This circuit, shown in Figure 2.15, is called a full adder because it includes the incoming carry in the calculation. A half adder adds only the two data bits without an incoming carry:

Figure 2.15: Full adder circuit

The full adder uses logic gates to produce its output as follows. The sum bit S is 1 only if the total number of bits with a value of 1 in the collection A, B, C_in is an odd number. Otherwise...

Clocking

The clock signal serves as the heartbeat of a processor. This signal is usually a square wave signal operating at a fixed frequency. A square wave is a digital signal that oscillates between high and low states, spending equal lengths of time at the high and low levels on each cycle. Figure 2.17 shows an example of a square wave over time:

Figure 2.17: Square wave signal

The clock signal in a computer system is usually generated from a crystal oscillator providing a base frequency of a few megahertz (MHz). 1 MHz is 1 million cycles per second. A crystal oscillator relies on the resonant vibration of a physical crystal, usually made of quartz, to generate a cyclic electrical signal. The mechanical vibration of the crystal is transformed into an electrical signal by the piezoelectric effect. The piezoelectric effect is the electrical charge that accumulates in certain crystals when placed under mechanical stress. Quartz crystals resonate at precise frequencies...

Sequential logic

Digital circuitry that generates outputs based on a combination of current inputs and past inputs is called sequential logic. This contrasts with combinational logic, in which outputs depend only on the current state of the inputs.

When a sequential logic circuit composed of several components operates those components under the control of a shared clock signal, the circuit implements synchronous logic.

The steps involved in the execution of processor instructions take place as a series of discrete operations that consume input in the form of instruction opcodes and data values received from various sources. This activity takes place under the coordination of a master clock signal. The processor maintains internal state information from one clock step to the next, and from one instruction to the next.

Modern complex digital devices, including processors, are almost always implemented as synchronous sequential logic devices. Low-level internal components...

Hardware description languages

It is straightforward to represent simple digital circuits using logic diagrams like the ones presented earlier in this chapter. When designing digital devices that are substantially more complex, however, the use of logic diagrams quickly becomes unwieldy. As an alternative to the logic diagram, several hardware description languages have been developed over the years. This evolution has been encouraged by Moore’s law, which drives digital system designers to continually find new ways to quickly make the most effective use of the constantly growing number of transistors available in integrated circuits.

Hardware description languages are not the exclusive province of digital designers at semiconductor companies; even hobbyists can acquire and use these powerful tools at an affordable cost. Some are even free.

A gate array is a logic device containing many logic elements such as NAND gates and D flip-flops that can be connected to form...

Summary

This chapter began with an introduction to the properties of electrical circuits and showed how components such as voltage sources, resistors, and wires are represented in circuit diagrams. The transistor was introduced, with a focus on its use as a switching element in digital circuits. The NOT gate and the AND gate were constructed from transistors and resistors. Additional types of logic gates were defined and truth tables were presented for each device. Logic gates were used to construct more complex digital circuits, including latches, flip-flops, registers, and adders. The concept of sequential logic was introduced, and its applicability to processor design was discussed. Finally, hardware description languages were introduced and a 4-bit adder example was presented in VHDL.

You should now understand basic digital circuit concepts and the design tools used in the development of modern processors. The next chapter will expand upon these building blocks to explore...

Exercises

1. Rearrange the circuit in Figure 2.5 to convert the AND gate to a NAND gate. Hint: there is no need to add or remove components.
2. Create a circuit implementation of an OR gate by modifying the circuit in Figure 2.5. Wires, transistors, and resistors can be added as needed.
3. Search the internet for free VHDL development software suites that include a simulator. Get one of these suites, set it up, and build any simple demo projects that come with the suite to ensure it is working properly.
4. Using your VHDL tool set, implement the 4-bit adder using the code listings presented in this chapter.
5. Add test driver code (search the internet for VHDL testbench to find examples) to your 4-bit adder to drive it through a limited set of input sets and verify that the outputs are correct.
6. Expand the test driver code and verify that the 4-bit adder produces correct results for all possible combinations of inputs.

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