By T.J. Stonham
1 Numerical illustration of information.- 2 Operations on binary data.- three Combinational common sense design.- four Sequential good judgment fundamentals.- five layout of sequential good judgment circuits.- 6 The electronic system.- 7 sensible electronic circuits.- solutions to difficulties.
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The minimization theorem is applicable to any minterms on the K-map that occupy adjacent cells. However by using the map alone, the variables that can be eliminated between a pair of minterms, can be detected, without having to resort to algebra. The procedure is as folIows. Neighbouring cells set to 1 are looped together as in Fig. 5. K-maps are considered to be continuous at their edges so minterms 1 and 5 are also adjacent and form loop 2. The function can now be described as being 'F = 1 if the inputs are in loop 1 or loop 2' .
Remember. In the 2nd canonical form 1->8 and O->B. 10) Ru/es for Looping on a Karnaugh Map 1. Loops must contain 2 n adjacent cells set to 1 (or 0 for the 2nd canonical form). A single cell (loop of 2°) cannot be simplified. A loop of 2 (2 1 ) is independent of 1 variable. A loop of 4 (22 ) is independent of 2 variables, and in general a loop of 2 n is independent of n variables. Therefore to obtain the simplest functions, use the largest possible loops. 2. All cells set to 1 must. be covered when specifying the minimal form of the function (0 for the 2nd canonical form).
The truth tables for both sides of the equation are calculated, and if they are identical for all input values, then the identity is true. B = A + B using truth tables. B = A + B The Principle of Duality A careful scrutiny of the Boolean theorems will reveal an interesting property. Most theorems occur in pairs and, given one theorem, the other can be obtained by interchanging all the AND and OR gates. B = A If the OR gate is replaced by AND and vice versa, the 2nd absorption theorem is 25 obtained.
Digital Logic Techniques: Principles and Practice by T.J. Stonham