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[...]... names NAND and NOR are contractions of NOT AND and NOT OR, respectively The NAND is generated by inverting the output of an AND function The symbols for the NAND gate and its equivalent circuit are shown in Figure 2.16 The algebraic expression for the NAND function is: Y ϭ AෆиෆB ෆෆෆ 2.3 • Derived Logic Functions 35 FIGURE 2.16 NAND Gate Symbols Table 2.6 NAND Function Truth Table A B Y 0 0 1 1 0 1... NAND gates combine the NOT and AND functions in a single circuit Similarly, NOR gates combine the NOT and OR functions Gates for more complex functions, such as Exclusive OR and Exclusive NOR, also exist We will examine all these devices later in the chapter NOT, AND, and OR Functions KEY TERMS Truth table A list of all possible input values to a digital circuit, listed in ascending binary order, and. .. a digital logic element The arrows at the input and output of the two IEEE symbols show inversion, like the bubbles in the distinctive-shape symbols FIGURE 2.1 Inverter Symbols AND Function Table 2.2 2-input AND Function Truth Table A B Y 0 0 1 1 0 1 0 1 0 0 0 1 KEY TERMS AND gate A logic circuit whose output is HIGH when all inputs (e.g., A AND B AND C) are HIGH Logical product AND function The AND. .. logic functions, AND, OR, and NOT, can be combined to make any other logic function Special logic gates exist for several of the most common of these derived functions In fact, for reasons we will discover later, two of these derived-function gates, NAND and NOR, are the most common of all gates, and each can be used to create any logic function NAND and NOR Functions The names NAND and NOR are contractions... the binary number 11001000001101001001 to hexadecimal 1.5 Digital Waveforms KEY TERM Digital waveform A series of logic 1s and 0s plotted as a function of time The inputs and outputs of digital circuits often are not fixed logic levels but digital waveforms, where the input and output logic levels vary with time There are three possible types of digital waveform Periodic waveforms repeat the same pattern... areas of electronics are analog and digital electronics Analog electronics deals with continuously variable quantities; digital electronics represents the world in discrete steps 2 Digital logic uses defined voltage levels, called logic levels, to represent binary numbers within an electronic system 3 The higher voltage in a digital system represents the binary digit 1 and is called a logic HIGH or logic... indicators of logic HIGH and LOW states • Describe those logic functions derived from the basic ones: NAND, NOR, Exclusive OR, and Exclusive NOR • Explain the concept of active levels and identify active LOW and HIGH terminals of logic gates 2.2 2.3 2.4 2.5 2.6 Basic Logic Functions Logic Switches and LED Indicators Derived Logic Functions DeMorgan’s Theorems and Gate Equivalence Enable and Inhibit Properties... Multiple-Input NAND and NOR Gates Table 2.8 shows the truth tables of the 3-input NAND and NOR functions The logic circuit symbols for these gates are shown in Figure 2.18 Table 2.8 3-input NAND and NOR Function Truth Tables A B C ෆෆиෆBෆиෆC Aෆෆෆෆ ෆෆϩෆBෆϩෆC Aෆෆෆෆ 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 The truth tables of these gates can be generated by understanding the... binary by sum of powers of 2 (add place values to get a total) or repeated division by 2 (divide by 2 until quotient is 0; remainders are the binary value) 8 The hexadecimal number system is based on 16 It uses 16 digits, from 0–9 and A–F, with power-of-16 multipliers 9 Each hexadecimal digit uniquely corresponds to a 4-bit binary value Hex digits can thus be used as shorthand for binary 10 A digital. .. nature and which digital? Explain your answers b 1000 g 111011 a Water temperature at the beach c 11001 h 1011101 b Weight of a bucket of sand d 110 i 100001 c Grains of sand in a bucket e 10101 j 10111001 d Waves hitting the beach in one hour e Height of a wave f People in a square mile Section 1.2 Digital Logic Levels 1.2 A digital logic system is defined by the voltages 3.3 volts and 0 volts For a . defined values, and digital volt- ages or currents can vary only by distinct, or discrete, steps. Some keywords highlight the differences between digital and analog electronics: Analog Digital Continuously. hexadecimal. 1.5 Digital Waveforms Digital waveform A series of logic 1s and 0s plotted as a function of time. The inputs and outputs of digital circuits often are not fixed logic levels but digital wave- forms,. waveform and its representation in both analog and digital forms. The analog voltage, shown in Figure 1.1b, is a copy of the original waveform and in- troduces distortion both in the storage and playback