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274 DIGITAL BUILDING BLOCKS AND COMPUTER SYSTEMS TABLE 6.1.1Representation of Numbers in Different Systems Base 10 Base 2 Base 8 ...
6.1 DIGITAL BUILDING BLOCKS 275 A A AB 00 01 10 11 F 0 1 1 1 F Off Off On On B F = A + B F = 1 (light is on) if either A or B (o ...
276 DIGITAL BUILDING BLOCKS AND COMPUTER SYSTEMS truth table. Similarly, the OR operation followed by the NOT operation is known ...
6.1 DIGITAL BUILDING BLOCKS 277 TABLE 6.1.2Logic Symbols and Truth Tables The last two entries in Table 6.1.3 are known asDeMorg ...
278 DIGITAL BUILDING BLOCKS AND COMPUTER SYSTEMS TABLE 6.1.3Basic Boolean Identities Identity Comments 1.X+ 0 =X Identities 1–9 ...
6.1 DIGITAL BUILDING BLOCKS 279 Solution The solution is given in Figure E6.1.4(b). A C F B (a) Figure E6.1.4 A A B A ⋅ C F = A ...
280 DIGITAL BUILDING BLOCKS AND COMPUTER SYSTEMS EXAMPLE 6.1.6 (a) Express DeMorgan’s laws given by X+Y=X·Y and X·Y=X+Y in terms ...
6.1 DIGITAL BUILDING BLOCKS 281 Thus far we have shown how to find the truth table for a given combination of logic blocks. The ...
282 DIGITAL BUILDING BLOCKS AND COMPUTER SYSTEMS BD A + B A CD Half-adder C X C Z W Full adder Y BD A Half- adder C C B W X D A ...
6.1 DIGITAL BUILDING BLOCKS 283 A D C B A B (a) A B A D C B A B (b) Figure E6.1.7 The basic logic gates described earlier are us ...
284 DIGITAL BUILDING BLOCKS AND COMPUTER SYSTEMS function, its SOP form can be obtained by taking the sum of the minterms that c ...
6.1 DIGITAL BUILDING BLOCKS 285 Noting thatFhas an output of 0 that corresponds to maxtermsM 0 ,M 2 ,M 4 , andM 5 ,Fcan therefor ...
286 DIGITAL BUILDING BLOCKS AND COMPUTER SYSTEMS for example, has an assignment ofA ̄·B ̄·C·D( ̄ = 0 · 0 · 1 · 0 ), whereas them ...
6.1 DIGITAL BUILDING BLOCKS 287 EXAMPLE 6.1.10 Consider a Boolean functionF(A, B, C, D) defined by the K map of Figure E6.1.10(a ...
288 DIGITAL BUILDING BLOCKS AND COMPUTER SYSTEMS Let us now illustrate the application of this procedure in the following exampl ...
6.1 DIGITAL BUILDING BLOCKS 289 as adon’t-care outputbecause of a physical constraint. As another example, Figure 6.1.16 shows t ...
290 DIGITAL BUILDING BLOCKS AND COMPUTER SYSTEMS (c) 01 11 10 00 00 01 11 AB CD 10 1 11 d CD⋅ 1 d d d d d BC⋅ AD⋅ (d) 01 11 10 0 ...
6.1 DIGITAL BUILDING BLOCKS 291 instruction should not be used. Figure 6.1.17(b) summarizes the specification for an SRFF in ter ...
292 DIGITAL BUILDING BLOCKS AND COMPUTER SYSTEMS an output and then go back to check it for self-consistency. This is given as a ...
6.1 DIGITAL BUILDING BLOCKS 293 EXAMPLE 6.1.14 The positive-edge triggered D flip-flop is given the inputs shown in Figure E6.1. ...
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