Markdown All in One by Yu Zhang
Markdown Table Prettifier by Krisztian Daroczi
Markdown+Math by goessner
Google Chrome -> print to pdf -> A4, Portrait,
 
234567891123456789212345678931234567894123456789512345678961
--------|---------|---------|---------|---------|---------|-

Laws and Theorems of Boolean Algebra

binary function list

nr. f(a,b) 00 01 10 11
0 nul 0 0 0 0
1 and 0 0 0 1
2 > 0 0 1 0
3 a 0 0 1 1
4 < 0 1 0 0
5 b 0 1 0 1
6 != 0 1 1 0
7 or 0 1 1 1
8 nor 1 0 0 0
9 == 1 0 0 1
10 !b 1 0 1 0
11 >= 1 0 1 1
12 !a 1 1 0 0
13 <= 1 1 0 1
14 nand 1 1 1 0
15 collapse 1 1 1 1

Use Python to proove or deny the rule according to your variant.

  1. x⋅0=0x \cdot 0 = 0
  2. x+1=1x + 1 = 1
  3. x⋅1=xx \cdot 1 = x
  4. x+0=xx + 0 = x
  5. x⋅x=xx \cdot x = x
  6. x+x=xx + x = x
  7. x⋅x‾=0x \cdot \overline{x} = 0
  8. x+x‾=1x + \overline{x} = 1
  9. x‾‾=x\overline{\overline{x}} = x
  10. x⋅y=y⋅xx \cdot y = y \cdot x
  11. x+y=y+xx + y = y + x
  12. x(yz)=(xy)z=(xz)y=xyzx(yz)=(xy)z=(xz)y=xyz
  13. x+(y+z)=(x+y)+z=(x+z)+y=x+y+zx+(y+z)=(x+y)+z=(x+z)+y=x+y+z
  14. x⋅(y+z)=x⋅y+x⋅zx \cdot (y+z)=x \cdot y + x \cdot z
  15. x+y⋅z=(x+y)⋅(x+z)x + y \cdot z=(x+y) \cdot (x+z)
  16. x⋅y‾=x‾+y‾\overline{x \cdot y}=\overline{x}+\overline{y}
  17. x+y‾=x‾⋅y‾\overline{x + y}=\overline{x}\cdot\overline{y}
  18. x⋅(x+y)=xx \cdot (x + y) = x
  19. x+x⋅y=xx + x \cdot y = x
  20. (x+y)⋅(x+y‾)=x(x+y)\cdot(x+\overline{y})=x
  21. x⋅y+x⋅y‾=xx \cdot y + x \cdot \overline{y}=x
  22. (x+y‾)⋅y=x⋅y(x+\overline{y})\cdot y= x \cdot y
  23. x⋅y‾+y=x+yx \cdot \overline{y} + y= x + y
  24. (x+y)⋅(x‾+z)⋅(y+z)=(x + y) \cdot (\overline{x} + z) \cdot (y + z) = (x+y)⋅(x‾+z)(x + y) \cdot (\overline{x} + z)
  25. x⋅y+x‾⋅z+y⋅z=x \cdot y + \overline{x} \cdot z + y \cdot z = (x⋅y)+(x‾⋅z)(x \cdot y) + (\overline{x} \cdot z)
  26. x⊕y=(x+y‾)⋅(x‾+y)x \oplus y = (x + \overline{y}) \cdot (\overline{x} + y)
  27. x⊕y=x⋅y‾+x‾⋅yx \oplus y = x \cdot \overline{y} + \overline{x} \cdot y
  28. x⊕y=(x+y)⋅(x⋅y‾)x \oplus y = (x + y) \cdot (\overline{x \cdot y})
  29. (x≡y)=x‾⋅y‾+x⋅y(x \equiv y) = \overline{x} \cdot \overline{y} + x \cdot y
  30. x⊕y=(x+y)⋅(x‾+y‾)x \oplus y = (x + y) \cdot (\overline{x} + \overline{y})
  31. f(x,y)=x⋅f(1,y)+x‾⋅f(0,y)f(x,y)=x \cdot f(1,y) + \overline{x} \cdot f(0,y)

The Bit Player 2018 - Claude Shannon - Legendas PT-BR

https://www.youtube.com/watch?v=CCrpgUM_rYc

Edward Forrest Moore

https://en.wikidat.com/info/edward-f-moore

Find Errors (proove or deny:)

https://www.mi.mun.ca/users/cchaulk/misc/boolean.htm

Shannon's theorem

https://cseweb.ucsd.edu/classes/sp17/cse140-a/slides/lec2.pdf