By Richard Sandige, Michael Sandige
This article is meant for an introductory electronic layout path for college students on the freshman point; it is also meant for an introductory laptop layout path with meeting language programming for college students on the sophomore point. this article makes use of a spiral educating strategy via introducing a layout challenge after which, within the comparable bankruptcy or a later bankruptcy, both (1) reemphasizing an analogous innovations whilst a unique layout is gifted, or (2) operating an identical challenge utilizing a distinct process. this can be performed to extend the chance of retention.
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Because FXOR 5 0 for these expressions, the complement FXOR must be used when combining the Boolean expressions to form the Boolean function, or FX OR 5 X # Y 1 X # Y . Complementing both sides of the Boolean function FX OR 5 X # Y 1 X # Y results in the Boolean function FX OR 5 X # Y 1 X # Y . Apply DeMorgan’s theorem to the Boolean expression, and we obtain FX OR 5 1 X 1 Y 2 # 1 X 1 Y 2 . Either the first Boolean function we derived for FXOR using the 1s of function or the second Boolean function we derived for FXOR using the 0s of function can be used to design or implement a circuit for FXOR.
7 Truth table for function F1 (Decimal) X Y Z F1 0 0 0 0 1 1 0 0 1 0 2 0 1 0 1 3 0 1 1 0 4 1 0 0 0 5 1 0 1 1 6 1 1 0 1 7 1 1 1 1 The compact minterm forms for F1 are written as follows: F1(X,Y,Z) 5 Sm(0,2,5,6,7) Explicit compact minterm form for the 1s of the function F1 F1 1 X,Y, Z 2 5 Sm 1 1,3,4 2 Explicit compact minterm form for the 0s of the function F1 The Boolean equation for either F1 or F1 represents the truth table for the function F1. To write an implicit compact minterm form, simply leave off the m following the summation symbol.
15. • The purpose of including both function F_1s and function F_0s is to verify that both functions generate the same output when we run a simulation. So, F 5 F_1s 5 F_0s should be true. 15. 9. 15. 9 does, in fact, provide a correct design for Boolean function F—that is, F 5 F_1s or F 5 F_0s can be used to generate the function F. 9. 9 that f_1s 5 1 for m3, m5, and m6, else f_1s 5 0. 9 that f_0s 5 0 for m0, m1, m2, m4, and m7; else, f_0s 5 1. 5 MORE ABOUT LOGIC GATES In this section we summarize some additional information about gates.