LOGIC7_r2 - Microwave & Communication Lab....

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Unformatted text preview: Microwave & Communication Lab. Chapter 7 Multi-Level Gate Networks NAND & NOR Gates Microwave & Communication Lab. The maximum number of gates cascaded in series between a network input and the output is referred to as the number of levels of gates. Thus, a function written in sum-of-products form or in product-of-sums forms corresponds directly to a two-level gate network, i.e. , Sum-of-products AND-OR 2-level network Products-of-sums OR-AND 2-level network Multi-Level Gate Networks Microwave & Communication Lab. EX : Z=(AB+C)[(D+E)+FG]+H 4 levels 7gates A C D E F F G H 1 2 3 4 B Microwave & Communication Lab. We can change Z expression as Z=AB(D+E)+C(D+E)+ABFG+CFG+H A B D E C F G 1 2 3 3 le v e ls 6 g a te s Microwave & Communication Lab. Remark: 1.Usually, variables and their complements are available as network inputs. Therefore, invertors will not normally be counted as a level . 2.The number of levels in an AND-OR(OR-AND) network can usually be increased by factoring (multiplying out some of terms) the sum-of-products (products-of-sums) expression . Microwave & Communication Lab. EX : Z = (A+B+C)(D+E)(B+F) 2 levels , P.O.S = [(A+B)(D+E)+C(D+E)](B+F) = (A+B)(D+E)(B+F)+C(D+E)(B+F) 3 levels , S.O.P Microwave & Communication Lab. EX : Find a network of AND and OR gates to realize F(a,b,c,d) = m(1,5,6,10,13,14) Sol : By karnaugh map method CD AB 00 01 11 10 0 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 f= acd+bcd+bcd+acd Microwave & Communication Lab. (1 ) D irectly n etw o rk 2 lev els , 5 gates a' c' d b c' d b c d' a c d' F Microwave & Communication Lab. (2) Factoring 3 levels 5 gates f=cd(a+b)+cd(a+b) c ' d c d ' a ' b a b f Microwave & Communication Lab. 1 NAND Gate : F=(AB) = A+B ? = A B F A B F F A B Other Types of Logic Gates Microwave & Communication Lab. A B F 0 0 1 0 1 1 1 0 1 1 1 N-inputs NAND Gates F = (x 1 x 2 x N ) = x 1 +x 2 + +x N F X1 X2 X3 . . Xn Microwave & Communication Lab. 2 N O R G ate : F=( A +B ) = AB = A B F A B F F A B Microwave & Communication Lab. A B F 0 0 1 0 1 0 1 0 0 1 1 0 N-inputs NOR Gates F = (x 1 +x 2 + +x N ) = x 1 x 2 x N X1 X2 X3 . . Xn F Microwave & Communication Lab. Fm = ABC+ABC+ABC+ABC =AB+AC+BC =(AB+AC+BC) By inspection of the table Fm=F M =(A+B)(A+C)(B+C) Microwave & Communication Lab. 3 M ajority Gate : A m ajority gate has odd num ber of inputs , and its output is 1 iff the m ajority of its inputs are 1 ....
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LOGIC7_r2 - Microwave & Communication Lab....

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