Purpose Introduction Readings LOGIC STATES LOGIC GATES Figure 9.2 Basic Logic Gates BOOLEAN ALGEBRA Fundamental laws Equality Associative Laws Distributive Laws DeMorgan’s Theorems Example of ProofExample of simplification Example with many input variables MEMORY ELEMENTS AND FLIP-FLOPS RS (Reset-Set Memory) Element JK Flip-Flops (TTL 74107) 555 Timer and digital clock Problems New Apparatus and Methods USING 7400 SERIES TTL CHIPS Experiment LED TESTING TRUTH TABLES FOR TTL GATES EXCLUSIVE OR THE RS FLIP-FLOP TTL CLOCK THE JK FLIP-FLOPPhysics 3330 Experiment #9 Fall 2006 Digital Electronics I: Logic, Flip-Flops, and Clocks Purpose This experiment introduces some of the fundamental circuit elements of digital electronics. These include three kinds of logic gate, two kinds of flip-flop (single bit memory), and the 555 timer chip used as a digital clock. Introduction In almost all experiments, the signals that represent physical quantities start out as analog waveforms. To display and analyze the information contained in these signals, they must be converted to digital data. Often this is done inside a commercial instrument such as an oscilloscope or a lock-in amplifier, which is connected to a computer through a digital interface. In other cases data acquisition cards are added to a computer chassis and the analog signals can be connected directly to the computer. Scientists usually buy their data acquisition equipment rather than build it, so they often don’t have to know too much about the digital circuitry that makes it work. Almost all data is analyzed with a computer, but like other users scientists don’t often have to know much about the digital circuitry inside their computers. We emphasize analog electronics in the course because scientists usually have to know much more about it to design and build their experiments. On the other hand, there are plenty of reasons to know something about digital methods. The author of our text (physicist Paul Horowitz) has built custom digital signal processors to search for signs of extraterrestrial intelligence in radio telescope signals, and particle physicists have built customized computer hardware to make calculations in quantum chromodynamics (the theory of the strong force). If you try to repair a commercial instrument like a modern lock-in you will find that it is full of digital electronics. The trend in modern instrument design is to do as much digitally as possible; even the front-panel knobs are not really analog controls, rather they are coded switches or optical encoders that generate digital data directly. An increasing number of analog parts can be controlled digitally, for example you can buy digital potentiometers that behave exactly like an analog pot, but look more like an op-amp chip, and instead of controlling the position of the wiper with a knob, you send a digital code into some of the extra pins. In digital circuits the voltage on a wire takes one of only two values called logic HIGH and logic LOW, corresponding to a binary 1 or 0. Information is conveyed by the pattern of HIGH and LOW voltages. A single wire can convey just one bit of information at any one time. When the information to be conveyed requires more than a single bit, either more wires can be used to convey data (parallel digital data), or a sequence of bits can be sent over time as HIGH’s and LOW’s moving along a single wire (serial digital data). Analog information can be translated into digital form by a device called an Analog-to-Digital Converter (ADC). A set of N bits has 2N possible different values. If you try to represent an analog voltage by 7 bits, your uncertainty will be about 1%, since there are 27 = 128 possible combinations of 7 bits. For higher accuracy you will need more bits. There is also a device called a Digital-to-Analog Converter (DAC) that can convert digital data back into an analog Experiment #9 9.1 Fall 2006waveform. You can choose either serial or parallel ADCs and DACs, depending on whether you are using serial or parallel digital data. In this experiment, we will learn about the most basic elements of digital electronics, from which more complex circuits, including computers, can be constructed. Logic gates perform logical operations like AND and OR. The gates we will use are made of bipolar transistors and they come from a family of devices called TTL (transistor-transistor logic). There are many other logic families (some made of MOSFETs) offering various trade-offs between speed, power consumption, supply voltage, and output drive capability (see H&H 9.01, and for the most recent families see the Logic Selection Guide at Texas Instruments, www.ti.com). Logic gates alone can be used to construct arbitrary combinatorial logic (they can generate any truth-table), but to create a machine that steps through a sequence of states like a computer does, we need also memory and a clock. The fundamental single-bit memory element of digital electronics is called a flip-flop. We will study two types, called SR (or RS) and JK. The flip-flops we have chosen are also from the TTL family. A digital clock is a repeating digital waveform used to step a digital circuit through a sequence of states. We will introduce the 555 timer chip and use it to generate a clock signal. Digital circuits able to step through a sequence of states with the aid of flip-flops and a clock are called sequential logic. Readings 1. Horowitz and Hill Chapter 8. Everything is this chapter is good to know about, but you can get by with just sections 8.01, 8.02, 8.04, 8.07-8.10, 8.12, 8.16. Also have a look at section 5.14 on the 555 timer chip. 2. (Optional) Diefenderfer 11.1-11.5, 12.1-12.5; Brophy Ch. 9 and pages 272-290; The TTL Cookbook, by Don Lancaster, SAMS (1974). Experiment #9 9.2 Fall 2006Theory - Electronic Logic and Boolean Algebra LOGIC STATES The voltage in a digital circuit is allowed to be in only one of two states: HIGH or LOW. We usually abbreviate these as HI and LO. 00.82.85.0VoltsTimeHIGtypical 0.4 LOTransition from LOW to Figure 9.1 TTL logic levelstypical 3.5 HI is taken to mean logical (1) or logical TRUE. LO is taken to mean logical (0) or logical FALSE. In the TTL logic family (see Figure 9.1), any voltage in the range 2.8 to 5.0 V is HI, and any voltage in the range 0 to 0.8 V is LO. Any voltage outside this range is undefined, and therefore illegal, except briefly during