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SFU - CMPT 150 - Lectures - Week 2

# SFU - CMPT 150 - Lectures - Week 2 - c A.H.Dixon CMPT 150...

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Unformatted text preview: c A.H.Dixon CMPT 150: Week 2 (Jan 14 - 18, 2008) 8 3.2 Logic Diagram to Function Table 1. Construct a function table with 2 n rows, where n is the number of inputs. Assign a distinct input sequence to each row. 2. For each row, assign the corresponding input sequence to the external inputs of the logic diagram. 3. Using the function table associated with each component, propagate a value along the internal signal lines until an output is determined. Record the output on the right-hand side of the function table. 4. Repeat steps (2) and (3) until a value has been assigned to each row. NOTE: The table can be constructed using DesignWorks by simply observing the value generated in the schematic at step (3) for each input sequence assigned. To illustrate, consider a simulation of the following schematic: g z x y z x y g c A.H.Dixon CMPT 150: Week 2 (Jan 14 - 18, 2008) 9 Its function table is determined to be: x y z f 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3.2.1 Symbolic Representation to Function Table 1. Construct a function table with 2 n rows, where n is the number of inputs. 2. For each row, assign the corresponding input values to the labels in the Boolean expression. 3. Evaluate the Boolean expression to obtain a value for that row, using the function tables of the operators in the expression. 4. Repeat these steps for all rows of the table. For example, the system defined by (x · y)+(y · z’) has the following function table: x y z (x · y)+(y · z’) f (0 · 0)+(0 · 1) 1 (0 · 0)+(0 · 0) 1 (0 · 1)+(1 · 1) 1 1 1 (0 · 1)+(1 · 0) 1 (1 · 0)+(0 · 1) 1 1 (1 · 0)+(0 · 0) 1 1 (1 · 1)+(1 · 1) 1 1 1 1 (1 · 1)+(1 · 0) 1 3.2.2 Function Table to Symbolic Representation It is important to recognize that the behavior of a digital system can be realized in many ways. Each way corresponds to a different symbolic representation. How- ever, all symbolic representations of the same behavioral description will have the same function table. c A.H.Dixon CMPT 150: Week 2 (Jan 14 - 18, 2008) 10 Thus it is possible to compare two digital systems for equivalence by comparing their function tables. However this is not usually practical, either because the tables are too large or because the inputs and outputs are labeled differently and therefore the rows and columns may need to be permuted before they can be compared. An alternative strategy is to see if the symbolic representation of one system can be transformed into the symbolic representation of the second. In the previous two examples, one can observe that their function tables are identical and therefore the symbolic representations define digital systems with the same behavior. Since the symbolic representations for these two systems are: f = ( x · y ) + ( y · z ) g = y · ( x + z ) it must be possible to transform one symbolic expression into the other. To do so, however, it is necessary to know what the allowable transformation rules are.so, however, it is necessary to know what the allowable transformation rules are....
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SFU - CMPT 150 - Lectures - Week 2 - c A.H.Dixon CMPT 150...

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