By T.J. Stonham
1 Numerical illustration of information.- 2 Operations on binary data.- three Combinational good judgment design.- four Sequential good judgment fundamentals.- five layout of sequential common sense circuits.- 6 The electronic system.- 7 sensible electronic circuits.- solutions to difficulties.
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Extra info for Digital Logic Techniques: Principles and Practice
We start with the least significant bits of the input words. Taking one bit from each word and any carry from the previous stage, we add them together to produce an output sum bit, and a carry which is input to the next stage of the addition. This procedure is repeated for every binary place in the addition. The adder cell is therefore: ;th ce 11 where Ai and Bi are the external inputs, being the ith bits of the input words A and B, respectively. Ci_I is the carry-in from the previous cell, Ci is the carry-out to the (i + l)th cell and Si is an externaIoutput forming the ith bit of the sumo Functions Ci and Si can now be designed.
Note the 'CR followed by AND' structure. , BCC==~~ Inputs OR level AND level Output Fig. 2 A 2nd canonical form circuit. 33 For example: Input ABC = 000 gives F=O and forms the maxterm (A+B+C). Input ABC = 001 gives F=O and forms the maxterm (A+B+C) and so on. Compare this rule with the 1st canonical rule. It is the opposite in every respect. 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.
B. C By comparing the final NAND circuit with the original AND/OR version, the reader can see that the structure and interconnections are identical. The only difference between them is that every gate in the AND/OR version has been replaced with a NAND gate. There is however an exception to this behaviour. Ifthe 1st canonical form is not completely 2-level and any input does not pass through an AND gate, it must be inverted before the AND/OR gates are replaced with NANDS. Take, for example, the function F = A + BC which is a very simple 1st canonical form, where variable A goes directly to the output OR gate.