By Heinrich J. Stüttgen
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Extra resources for A Hierarchical Associative Processing System
25 to an equivalent fraction in base 2. 2. 25, is given in row 1. 25). On multiplying the fraction 5 in row 2 by the number 2, we obtain the result shown in row 3. Since the updated fraction is 0, the algorithm terminates. The equivalent fractional number in base 2 is obtained by (1) listing the whole parts from left to right in the order they are formed, and (2) appending a radix point to the left of the number. 44)10 to an equivalent fraction in base 5. 21)5. 7)10 to an equivalent binary fraction.
Another example of a Boolean expression is “x·y+z,” where x, y, and z are Boolean variables. We distinguish between two forms of Boolean expression and call them simple and compound expressions. We assume that simple expressions are composed of a constant, a Boolean variable, or a combination of these with a single Boolean operator. The expressions given in the definition are examples of simple Boolean expressions. We assume that compound expressions contain at 40 DIGITAL DESIGN AND COMPUTER ORGANIZATION least two Boolean operators.
1. In computing these expressions, we compute sub-expressions of each as needed. A sub-expression is an expression within the original larger expression. We then form the value of the expression from its component subexpressions. 2 Truth Table for the Boolean Expression xy+z x y z xya xy+zb 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 1 a Sub-expression xy. b Expression value obtained from applying the logical OR operation on the columns with label z and xy. 1. 2.
A Hierarchical Associative Processing System by Heinrich J. Stüttgen