By D. Protheroe;Douglas Lewin;D. Lewin
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Extra info for Design of Logic Systems
S. T The first step in the process is to form a table containing all possible combinations of the truth values (either 0 or 1) of the basic propositions M, Sand T. 3 that these are the normal combinations formed by three two-valued binary variables. These values are then substituted into the equations for Al and A 2 , and the resulting truth value of the equations entered in the table. e. 110, which is the symbolic representation of male, unmarried and over 35. _-------- 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 Al Az 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 1 Al = 1.
Examine the list to find the two lowest values of f. These two values are replaced by a composite frequency whose value is the sum of the pair replaced. 3. Repeat stage 2 until the list of frequencies has been reduced to a single value of 1, representing the sum of all the original frequencies. By this process, a tree of values may be pictured, with the 'root' successively branching out until the n separate 'leaves' are reached. The Huffman code for each of the original symbols is now constructed by starting at the root and labelling one of the branches with a 0 and the other with a 1.
S. T If we now apply the distributive law we have A = M. T(S + S) + S. T(M + M) + M. S. T Since A + if = 1 and A . T In other words applicants must be 1. male and under 35, or 2. married and under 35, or 3. female, unmarried, and over 35. Thus by representing the logical statements symbolically and applying the rules of logical algebra, we have arrived at a simpler statement of the original propositions. To show that these two equations are equivalent (which does, of course, follow directly from the algebra) we can use the truth table method.