Chapter 6: Difference between revisions

From Class Wiki
Jump to navigation Jump to search
Line 1: Line 1:
===Digital Logic===
===Digital Logic Gates===
{| class="wikitable" border="1" style="text-align:center"
{| class="wikitable" border="1" style="text-align:center"
|+Boolean Algebra
|+Boolean Algebra
Line 13: Line 13:
|}
|}


*'''NAND Equivalent Gates'''
===De Morgan Laws & NAND Equivalent Gates===
*"If the variables in a logic expression are replaced by their inverses, and if the AND operation is replaced by OR, the OR operation is replaced by AND, and the expression is inverted, the resulting logic expression yields the same values as before the changes."<ref>Electronics p.353</ref>
:*Inv: <math>\overline{AA}=\overline{A}</math>, Nand with the inputs tied together
*It is possible to create any combinatorial logic function with solely NAND (or NOR) gates
:*AND: <math>\overline{(\overline{AB})}</math>, NAND followed by and Inv
:*OR: <math>\overline{(\overline{A} \, \overline{B})}=A+B</math>
:*Inv: <math>\overline{A}=\overline{AA}</math>
:*AND: <math>AB=\overline{(\overline{A}+\overline{B})}</math>
*De Morgan Laws
:*OR: <math>A+B=\overline{(\overline{A} \, \overline{B})}</math>
:*

:*
===References===
<references/>

Revision as of 20:28, 23 March 2010

Digital Logic Gates

Boolean Algebra
A B NAND
NOR
XOR
0 0 1 1 0
0 1 1 0 1
1 0 1 0 1
1 1 0 0 0

De Morgan Laws & NAND Equivalent Gates

  • "If the variables in a logic expression are replaced by their inverses, and if the AND operation is replaced by OR, the OR operation is replaced by AND, and the expression is inverted, the resulting logic expression yields the same values as before the changes."<ref>Electronics p.353</ref>
  • It is possible to create any combinatorial logic function with solely NAND (or NOR) gates
  • Inv:
  • AND:
  • OR:

References

<references/>