Gate Design

Module 4

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Inverting and Non-inverting gates

Logic Types

• Positive logic
• 1 represents true
• 0 represents false
• ex: AND and OR
• Negative logic
• 0 represents true
• 1 represents false
• ex: negative logic AND

A B	A B	AND	AND
F F  F T  T F  T T	1 1  1 0  0 1  0 0	F   F   F   T	1   1   1   0

• negative logic OR

A B	A B	OR	OR
F F  F T  T F  T T	1 1  1 0  0 1  0 0	F  T  T  T	1  0  0  0

• Mixed logic
• combination of positive logic and negative logic
• ex: NAND and NOR
• inputs are positive logic
• outputs are negative logic

Pos. Logic NAND		Mixed Logic AND
		Pos. Logic In		Neg. Logic Out
A B	F	A B	A B	Function	Function
0 0   0 1   1 0   1 1	1   1   1   0	F F  F T  T F  T T	0 0  0 1  1 0  1 1	F   F   F   T	1   1   1   0

Why use mixed logic?

• Allows implementations that retain the readability of the function while allowing
• Implementation in specified gate types
• Implementation in specified signal activation levels

Why is implementation in specified gate types important?

• VLSI approach - NANDs and NORs are easily designed using switch level logic, while ANDs and ORs require 2 extra switches

Why is implementation of different signal activation levels important?

• Some functions are most easily understood using negative logic
• Example: clear - a logic zero sets the clear, however, we want to know what is going to make that happen
• Such signals are called active low
• Active low signals denoted on schematic by bubbles
• Some functions are most easily understood using positive logic
• These signals are called active high
• Active high signals denoted on schematic by absence of a bubble

Synthesis: Implementing Boolean equations using mixed logic

· Implement Boolean equation using ANDs and ORs, ignoring all bars

· Put in slashes to indicate the location of the bars

· Implement all gate restrictions

o starting from the input signals replace all gates with the required physical gate type: remember the DeMorgan equivalent gates!

o be sure to replace positive logic AND gates with the desired mixed logic AND gate and positive logic OR gates with the desired mixed logic OR gate, ex: implement circuit using only NOR gates

· Balance bubbles and/or slashes

o there should be an even number of bubbles on each line

o if there is not, inverters must be added to balance the bubbles

o use the appropriate inverter so that bubbles "cancel each other out"

· Example

· Inclusion of active low signals

· Example

Analysis: Specifying the Boolean function from a mixed logic circuit

· Make sure all lines are balanced (bubbles)

· Read off function

o Pay attention to the positive logic gate type (AND / OR only) and slashes

o Ignore all bubbles

o Slashes indicate the output of the gate is negated

· Example

· Inclusion of active low signals

· Example

Question, comments or problems with this page to Sudhakar Yalamanchili