Logic gates Boolean - FIGURE 5-25 Single—variable x theorems(1 x 0 = 0 0 0 X(2 x 1 = x x T X(3 x x = x X X(4 x-§=0 0 X(5 x 0=x x 0 x(6 X 1=1 T'1

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Unformatted text preview: FIGURE 5-25 Single—variable x theorems. (1) x . 0 = 0 0 0 X (2) x - 1 = x x T X (3) x - x = x X X (4) x-§=0 0 X (5) x+0=x x 0 x (6) X+1=1 T '1 x (7) X+x=x x . : x (8) X+§=1 1 Multivariable Theorems The theorems presented below involve more than one variable: . (9) x+y=y+ x C0mmU+a+'0“<(10) x-_y=y-x (11) x+(y+z)=(x+y)+z=x+y+z A s S go‘a-h‘lh < (12) amyz) = (An/)2 = xyz" . . . <13a>x<y+z>=xy+xz D457") 5’110”<(13b) (w+x)(y+z)=wy+x3'+wz+xz (14) x+xy=x (15) x+Iy=x+y DEMURGANS 'l‘lll‘JORIGMS BOOLEAN THEOREMS 1. x-O-O 2. x-1=x 3. x-x=x 4. x-iao 5. x+0=x 6. x+1=1 7. x+x=x 8. x+§=1 9. x+y=y+x 10. x-ysy-x 11. x+1v+11a1x+v1+zux+v+z 12. xtyz)=(xy)z=xyz 30. x(y+z)=xy+xz 13h. 1w+x11y+llswy+xv+wz+xz 14. x+xy=x 16. x+§y=x+y 16. x+yai§ 17. fi=i+7 LOGIC GATE TRUTH TABLES on NOR AND NAND EX-OFI EX-NOR A+B A+B A-B “A48 A93 A68 agi- o 1 o 1 1 1 o 3 1 1 o ._ 1 o 1 H.400) dO—‘Dw LOGIC GATE SYMBOLS A x=A+B A x=A+B B 8 OR Gate NOR Gate A A x=AB x-=AB B B AND Gate NAND Gate EX-OR EX-NOR ...
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This note was uploaded on 05/10/2008 for the course SEE SEE103 taught by Professor Trinh during the Spring '08 term at A.T. Still University.

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Logic gates Boolean - FIGURE 5-25 Single—variable x theorems(1 x 0 = 0 0 0 X(2 x 1 = x x T X(3 x x = x X X(4 x-§=0 0 X(5 x 0=x x 0 x(6 X 1=1 T'1

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