61 1. Since there are other techniques for minimizing Boolean functions, what's the overriding reason for using Karnaugh maps? fne Karnaugh map is the least costly to implement. fit) (2) No other techniques work. (3) Patterns of the element minterm combinations can quickly be seen by the eye, which leads to a minimization. (4) Only a paper pencil and are required for implementing the technique. 2. For the Karnaugh map in Fig. fi4, what's the corresponding minimum Boolean function? -' (l) f=Ac-+BA+ee (2) =e+AB f (3) f=e+ABc (4) =Ac+Agc+en f AE t,/,^,-l;T t y4) bs ABI+ t,{, A s t I 000r il t0 -- -) I ,6 A 0 l0 I I I +^ ( ? t I I Fig. I 14 3. Minimize the previous. Karnaugh map assuming that mr (ABC) has a "don't care" mapped into it. (1) f=A+e *rz) r=e +AB (3) f=Ae +AB+ne =A+Ae (4) f 4. In using the Kamaugh map, we leave certain boxes blank and put the logic "1" symbol in the other boxes. What do these blank boxes represent? (1) The function isn't defined for these input combinations. (2) These boxes are not minterms. (3) These boxes are reserved for "don't care" terms. (4) These represent "0"s boxes the logic of the function. S 5. Minimize the Karnaugh map in Fig. 1i5. (l) f=AB+eED+ABC+AeD =BD+Aeo+AeD+ABC (2) f f=BD+Ae+etD+ABC *(3) =AB @) f +BD+ABeD+ABCI ol AB I CD 00 0l tl t0 0 4 t2 I 00 I I 5 r3 9 0l I I _] 5 7 l5 tl I I 2 6 t4 lo !I t0 I Fig. 115 I the previous Karnaugh given 6. Minimize map that minterms rrlr, rrrs, &rtd mr: become don't cares. ( 1) f= n_D_ + B_e_D + ABC [B_+ I =4E+EP+CD+ABC (2) f (3) = f BD +ABD +ABCD +ABC +ABD I (4) =As f + BD +AeD +AeD + BCD +ABD 7. A popular code for data representation is the hexadecimal code. I Basically, it's identical to the BCD code for decimal inputs 0-9; however, it makes use of the decimal inputs 10-15 by assigning the first letters (You'll six of the alphabet, A-F, to these inputs. recall that in the I standard BCD code these terms aren't used.) This creates a...
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