1. CEC 220 Digital Circuit Design NAND/NOR Multi-Level Circuits
Wed, February 12
CEC 220 Digital Circuit Design

2. CEC 220 Digital Circuit Design
Lecture Outline
The Eight Basic Two-Level Circuits
NAND/NOR Multi-Level Gate Circuits
Design of Two-Level, Multiple-Output Circuits
Multiple Output NAND/NOR Circuits
Wed, February 12
CEC 220 Digital Circuit Design

3. NAND/NOR Multi-Level Circuits The Eight Basic Two-Level Circuits
Assume that we are given the following K-Map(s)
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AB CD 00 01 11 10 1
SOP
POS
Wed, February 12
CEC 220 Digital Circuit Design

4. NAND/NOR Multi-Level Circuits The Eight Basic Two-Level Circuits
Two Level SOP Circuits
AND OR
NOR OR
NAND NAND
OR NAND
Wed, February 12
CEC 220 Digital Circuit Design

5. NAND/NOR Multi-Level Circuits The Eight Basic Two-Level Circuits
Two Level POS Circuits
OR AND
NAND AND
NOR NOR
AND NOR
Wed, February 12
CEC 220 Digital Circuit Design

6. NAND/NOR Multi-Level Circuits NAND Multi-Level Gate Circuits
Procedure for designing a minimum multi-level NAND-NAND circuit
Find a minimum SOP expression for f.
Draw the corresponding multi-level AND-OR circuit
Replace all gates with NAND gates leaving the gate interconnections unchanged.
Leave the inputs to levels 2,4,6, … unchanged.
Invert any literals which appear as inputs to levels 1,3,5 … .
Wed, February 12
CEC 220 Digital Circuit Design

7. NAND/NOR Multi-Level Circuits NAND Multi-Level Gate Circuits
An Example
AND & OR Network
NAND-NAND network
Wed, February 12
CEC 220 Digital Circuit Design

8. NAND/NOR Multi-Level Circuits NOR Multi-Level Gate Circuits
Procedure for designing a minimum multi-level NOR-NOR circuit
Find a minimum POS expression for f.
Draw the corresponding multi-level OR-AND circuit
Replace all gates with NOR gates leaving the gate interconnections unchanged.
Leave the inputs to levels 2,4,6, … unchanged.
Invert any literals which appear as inputs to levels 1,3,5 … .
Wed, February 12
CEC 220 Digital Circuit Design

9. NAND/NOR Multi-Level Circuits NOR Multi-Level Gate Circuits
An Example
AND & OR Network
NAND-NAND network
Wed, February 12
CEC 220 Digital Circuit Design

10. CEC 220 Digital Circuit Design
NAND/NOR Multi-Level Circuits Design of Two-Level, Multiple-Output Circuits
AB CD 00 01 11 10 1
AB CD 00 01 11 10 1
AB CD 00 01 11 10 1
A total of 9 gates
Wed, February 12
CEC 220 Digital Circuit Design

11. CEC 220 Digital Circuit Design
NAND/NOR Multi-Level Circuits Design of Two-Level, Multiple-Output Circuits
AB CD 00 01 11 10 1
AB CD 00 01 11 10 1
AB CD 00 01 11 10 1
A total of 7 gates
Wed, February 12
CEC 220 Digital Circuit Design

12. NAND/NOR Multi-Level Circuits Examples
Realize 𝑍=𝐴𝐵𝐶+𝐴𝐷+ 𝐶 𝐷 using as few 2-input NAND gates as possible
Assume that the inputs and their inverses are both available
AB CD 00 01 11 10 1
AB CD 00 01 11 10
Wed, February 12
CEC 220 Digital Circuit Design

13. NAND/NOR Multi-Level Circuits Examples
A combinational switching circuit has four inputs (A,B,C,D) and one output (F).
F=0 iff three or four of the inputs are 0.
Write the maxterm expansion for F and implement using a minimum three level AND & OR gates.
AB CD 00 01 11 10
AB CD 00 01 11 10 1
AB CD 00 01 11 10
Wed, February 12
CEC 220 Digital Circuit Design

14. NAND/NOR Multi-Level Circuits Examples
Realize 𝑓= 𝑎 𝑏 +𝑎𝑏𝑑+𝑎𝑐𝑑 using a three or more level NOR-gate circuit.
Wed, February 12
CEC 220 Digital Circuit Design

15. CEC 220 Digital Circuit Design
Next Lecture
Timing Diagrams
Multiplexers
Tri-State Buffers
Wed, February 12
CEC 220 Digital Circuit Design