Digital Logic Techniques: Principles and Practice by T.J. Stonham

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 functional electronic circuits.- solutions to difficulties.

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For example, in BCD coding, where decimal digits are represented in pure binary, the numbers 10102 to 1111 2 are never used; therefore the outputs of any logic system being driven by BCD encoded data would be 'don't cares' for these inputs. Obtain the minimal NAND and NOR logic functions to drive the top horizontal bar of a seven segment display from a BCD input. [A 7-segment display comprises 7 light emitting bars a - g Each bar lights up when a logical1 is applied to it. ] a bHc f e 9 The logic function Fa' to drive bar a, is dependent on four binary inputs ABCD.

The rule for obtaining the 2nd canonical form is therefore: for each entry in the truth table with an output at 0, create an OR of the inputs using the normal variable, if its value is 0, or its inverted value, if the input is at '1. The output of the OR gates are ANDed together to give the final output. Shorthand Notation Jor the 2nd Canonical Form Compare with 1st canonical form, where the normal variable implied 1 and the inverted variable implied O. The 2nd form can be represented as a set of numbers identifying the maxterms.

Remember F = 0 for a maxterm. F AB C 00 01 11 10 0 10 12 16 14 1 11 03 07 Os Note the cell addresses. 37 Minimization oj canonical jorms using Karnaugh Maps A K-map of a logic function can be used to obtain the simplest version of either the 1st or 2nd canonical form. Consider the 3-variabled logic function F = 1: (1,2,5,6). Its K-map is F AB C 00 01 11 10 0 00 12 16 o. 8. However, it still retains the AND/OR structure of a 1st canonical form function. 8) Applying the minimization theorem XY + Xy = X to minterms 2 and 6, where X = BC and Y = A, terms ABC + ABC become BC, which is a considerable simplification.

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