By Shimon P. Vingron
ISBN-10: 3642276571
ISBN-13: 9783642276576
Pt. 1. Combinational Circuits -- good judgment Variables and occasions -- Switching units -- common good judgment features -- common types -- Karnaugh Maps -- Adjacency and Consensus -- Algebraic Minimisation -- layout by way of Composition -- pt. 2. Latches -- uncomplicated conception of Latches -- Designing suggestions Latches -- simple Latches -- Latch Composition -- pt.3. Asynchronous Circuits -- Word-Recognition Tree -- Huffman's stream desk -- State-Encoding via Iterative Catenation -- Circuit research -- nation aid -- Verifying a good judgment layout
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Additional resources for Logic circuit design : selected methods
Example text
Then the connective ı is said to be idempotent if A ı A , A. Both AND and OR are idempotent, meaning A ^ A , A and A _ A , A. AND OR EQU XOR A^0,0 A_1 ,1 A$0,A A˚1,A A^1,A A_0 ,A A$1,A A˚0,A A^A,A A_A ,A A$A,1 A˚A ,0 A^A,0 A_A ,1 A$A,0 A˚A ,1 a b c d Fig. A,1 c Fig. 12 The single-variable formulas for NAND, NOR and IMPLICATION 36 3 Elementary Logic Functions As you can see from Fig. , A $ 1 , A and A ˚ 0 , A. But, note that neither EQUIVALENCE nor XOR are idempotent. The last pair of commutative logic functions consists of NAND and NOR, their single-variable formulas being found in Fig.
Among the more important aspects of the K-map, as the Karnaugh map is frequently called, are the following points discussed in this chapter: • Introduce and visualise Karnaugh sets (K-sets); • Develop new theorems, and prove given ones; • Directly calculate the AND-to-OR and OR-to-AND formulas in their simplified form. There are a number of further applications and modifications of the K-map, some discussed as we go along. 1 How to Draw a Karnaugh Map A Karnaugh map is drawn as a rectangle subdivided into rows and columns by input variables.
4) eD0 W The formulas starting with a multiple OR ( ) have the unwieldy name disjunctive canonical normal form which, following Dietmeyer (1971), we refer to as (canonical) AND-to-OR formulas. e/ of 1; when employing the conjunctive 1 The derivation of these formulas is discussed in-depth in Vingron (2004). 44 4 Normal Forms normal form, only the maxterms of those columns are conjuncted whose output value is 0. 5), and all the formulas for logic outputs in Chap. 2. 4), tend to yield unwieldy, excessively long, logical expressions and correspondingly complicated circuits as is shown when calculating a circuit for the events table of Fig.
Logic circuit design : selected methods by Shimon P. Vingron
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