EGR240 D5.1 BasicLogicGates info
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Basic Logic Gates
Discussion D5.1
Section 8.6.2Sections 13-3, 13-4
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Basic Logic Gates
and Basic Digital Design
• NOT, AND, and OR Gates
• NAND and N! Gates
• De"o#gan$s %&eo#e'
• ()clusi*e-! +! Gate
• "ultile-inut Gates
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N% Gate -- /n*e#te# X Y
01
10
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• Y = ~X (Verilog)
• Y = !X (ABEL)
• Y = not X (VHDL)
• Y = X’
• Y = X• Y = X (textook)
• not(Y,X) (Verilog)
N%
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N%
X ~X ~~X = X
X ~X ~~X
0 1 0
1 0 1
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AND GateAND
X
Y
Z
Z = X & Y
X Y Z
0 0 0
0 1 01 0 0
1 1 1
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• X & Y (Verilog " ABEL)
• X and Y (VHDL)
• X Y
• X Y
•X # Y
• XY (text$ook)
• and (Z%X%Y) (Verilog)
AND
U
V
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! Gate
'
X
Y Z
Z = X Y
X Y Z
0 0 0
0 1 11 0 1
1 1 1
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!
• X Y (Verilog)
• X Y (ABEL)
• X or Y (VHDL)
• X * Y (text$ook)
•X
V Y
• X U Y
• or(Z%X%Y) (Verilog)
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Basic Logic Gates
and Basic Digital Design
• N%, AND, and ! Gates
• NAND and NOR Gates
• De"o#gan$s %&eo#e'
• ()clusi*e-! +! Gate
• "ultile-inut Gates
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NAND GateNAND
X
Y
Z
X Y Z
0 0 1
0 1 11 0 1
1 1 0
Z = ~(X & Y)
nand (Z%X%Y)
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NAND Gate
N+,AND
X
Y
Z
- = X & Y
Z = ~- = ~(X & Y)
X Y - Z
0 0 0 1
0 1 0 11 0 0 1
1 1 1 0
-
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N! Gate
N'
X
YZ
X Y Z
0 0 1
0 1 01 0 0
1 1 0Z = ~(X Y)
nor(Z%X%Y)
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N! Gate
N+,'
X
Y
- = X Y
Z = ~- = ~(X Y)
X Y - Z
0 0 0 1
0 1 1 01 0 1 0
1 1 1 0
Z-
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Basic Logic Gates
and Basic Digital Design
• N%, AND, and ! Gates
• NAND and N! Gates
• DeMorgan’s Theorem
• ()clusi*e-! +! Gate
• "ultile-inut Gates
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NAND Gate
X
Y
X
Y
Z Z
Z = ~(X & Y) Z = ~X ~Y
=
X Y - Z
0 0 0 10 1 0 1
1 0 0 1
1 1 1 0
X Y ~X ~Y Z
0 0 1 1 10 1 1 0 1
1 0 0 1 1
1 1 0 0 0
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De "o#gan$s %&eo#e'-1
~(X & Y) = ~X ~Y
• N% all *a#iales• &ange to and to • N% t&e #esult
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N! Gate
X
YZ
Z = ~(X Y)
X Y Z
0 0 1
0 1 0
1 0 0
1 1 0
X
Y
Z
Z = ~X & ~Y
X Y ~X ~Y Z
0 0 1 1 1
0 1 1 0 0
1 0 0 1 0
1 1 0 0 0
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De "o#gan$s %&eo#e'-2
~(X Y) = ~X & ~Y
• N% all *a#iales• &ange to and to • N% t&e #esult
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De "o#gan$s %&eo#e'
• N% all *a#iales
• &ange to and to
• N% t&e #esult
• --------------------------------------------
• 7 + 7 +
• + 7 + 7 • 7 + 7 +
• + 7 + 7
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Basic Logic Gates
and Basic Digital Design
• N%, AND, and ! Gates
• NAND and N! Gates
• De"o#gan$s %&eo#e'
• Exclusive-OR (OR! Gate
• "ultile-inut Gates
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()clusi*e-! Gate
X Y ZXOR
XY
Z 0 0 0
0 1 1
1 0 1
1 1 0
Z = X . Y
xor(Z%X%Y)
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!
• X . Y (Verilog)
• X / Y (ABEL)
• X Y
• xor(Z%X%Y) (Verilog)
, 6 +te)t1oo9-⊕g
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()clusi*e-N! Gate
X Y ZXNOR
XY
Z 0 0 1
0 1 0
1 0 0
1 1 1
Z = ~(X . Y)
Z = X ~. Y
xnor(Z%X%Y)
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N!
• X ~. Y (Verilog)
• !(X / Y) (ABEL)
• X Y
• xnor(Z%X%Y) (Verilog)
, 6g e
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Basic Logic Gates
and Basic Digital Design
• N%, AND, and ! Gates
• NAND and N! Gates
• De"o#gan$s %&eo#e'
• ()clusi*e-! +! Gate
• Multi"le-in"ut Gates
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"ultile-inut Gates
Z1 2
3 4Z Z
Z
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"ultile-inut AND Gate
Z1
utut is :/G: onl; i< all inuts a#e :/G:Z1
An oen inut =ill <loat :/G:
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"ultile-inut ! Gate
utut is L> onl; i< all inuts a#e L>Z2
2Z
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"ultile-inut NAND Gate
utut is L> onl; i< all inuts a#e :/G:Z3
3Z
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"ultile-inut N! Gate
utut is :/G: onl; i< all inuts a#e L>Z4
4Z