By Hans W. Gschwind
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Veitch diagram" is used synonymously with "Karnaugh map". 26 3. 4) uses a normally closed contact of switch A, so that the light L is turned on, if the switch A is turned "off". ) b c Fig. 3. 4) The Venn diagram and the truth table should be self-explanatory. 4) permits us to state: the Light L is on if, and only if switch A is turned off. Consequently, we can make the statement: the light L is off, if the switch A is on. 4). 3. Functions of Two Variables Considering two binary variables, say A and B, we can have any one of the following four distinct conditions: I.
12. 1) A 0 B 0 X I 1 0 0 0 0 0 1 0 1 1 1 1 I 1 0 0 1 Fig. 13. Functional Diagram and Karnaugh Map for Sample Problem X + A 8 A C 8 c 8 c Fig. 14. Logic and Circuit Diagram for Sample Problem Let us now attempt to solve a problem which is not yet stated in Boolean algebra. Suppose we want to construct a circuit which gives an output if there are two or more of its three inputs present. 4* 52 4. Logic Circuits First, we construct a Karnaugh map. 5) The corresponding block and circuit diagrams are given in Fig.
Decoding of Digit 3 Fig. 18. Partial Matrix For reasons which will be immediately apparent, let us draw the circuits for a few digits in a somewhat unconventional manner as shown in Fig. 18. If we now draw all circuits and connect all points with the same label, we find the following diagram. 9 A A' ~~r-~~--~~~~~~~~~~~~~~~~---+----,_8 c ~~----~--~4-~~----7----r--~+-~~T-~~~~ C'~~--~~----4---~--~4-~~----+---~~~~~~ D ~~r-~~------r--4-+----4---~r----+--~+----+--~~- tl 7 7 8 g Fig. 19. Complete Decoding Matrix Such an arrangement is called a diode matrix.