Difference between revisions of "Chapter 6"

From Class Wiki
Jump to: navigation, search
(Digital Logic)
(Digital Logic)
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===
:*Inv: <math>\overline{AA}=\overline{A}</math>, Nand with the inputs tied together
+
*"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>
:*AND: <math>\overline{(\overline{AB})}</math>, NAND followed by and Inv
+
*It is possible to create any combinatorial logic function with solely NAND (or NOR) gates
:*OR: <math>\overline{(\overline{A} \, \overline{B})}=A+B</math>
+
:*Inv: <math>\overline{A}=\overline{AA}</math>
*De Morgan Laws
+
:*AND: <math>AB=\overline{(\overline{A}+\overline{B})}</math>
:*
+
:*OR: <math>A+B=\overline{(\overline{A} \, \overline{B})}</math>
:*
+
  +
===References===
  +
<references/>

Revision as of 19:28, 23 March 2010

Digital Logic Gates

Boolean Algebra
A B NAND
\overline{AB}
NOR
\overline{A+B}
XOR
A\oplus B
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: \overline{A}=\overline{AA}
  • AND: AB=\overline{(\overline{A}+\overline{B})}
  • OR: A+B=\overline{(\overline{A} \, \overline{B})}

References

<references/>