1. Logic gates

2. Computer Design using Digital Circuits
Primary circuit component is the “transistor”
Billions (literally) can be fabricated on a single integrated circuit (IC)
Circuits operate at low voltages (approx. one volt)
Transistors are used as simple switches
Transistors are connected together into circuits and turn each other on or off depending on how they’re connected
Circuit inputs and outputs are in either of two states, high (power supply) voltage, or low voltage (0V)
High state is a “one/true”, low state is a “zero/false"– Binary!!!

3. Electronic Design of a Digital Computer
General approach:
Wire together electronic components (transistors, in particular) to create gate level “building blocks”
Inverter, nand, nor, and more…
Use these “gates” to construct higher level modules that implement the basic functions of the computer

4. Boolean Algebra Based on symbolic logic
Designed by George Boole
Defines a set of operations on variables that have two states, true or false (or 1 and 0)
In symbolic logic, Boolean expressions are manipulated (similar to mathematical statements)
In circuit design, basic operations are represented with “logic gate” symbols

5. Basic Logical Operations (and gate symbols)
NOT
AND OR

6. NOT Inverts, or reverses, a Boolean value A’ !A 𝐀 ¬A A OUT F T
Truth Table
Symbolic representations: A’ !A 𝐀 ¬A

7. AND A B
OUT F T
Common representations:
Truth Table AB
A*B
A˄B

8. OR A B
OUT F T
Common representations:
Truth Table
A+B
A˅B

9. Additional Logical Operations
NOR
NAND
An “AND” followed by a “NOT”
An “OR” followed by a “NOT”
Note: The “bubble” means inversion (NOT)
These are easy to implement and commonly used in circuit design

10. NAND 𝐀𝐁 𝐀∗𝐁 𝐀˄𝐁 !(AB) ¬(A*B) A B OUT F T Truth Table
“nand” is the “not”, or inversion, of “and”

11. NOR 𝐀+𝐁 𝐀˅𝐁 !(A+B) ¬(A ˅ B) A B OUT F T Truth Table
“nor” is the “not”, or inversion, of “or”

12. (Mulit-input NANDs and NORs are easily implemented in a CMOS circuit)
More than 2 inputs?
3 input “AND”
AND = true if all inputs are true
OR = true if any inputs are true A B C
OUT F T
(Mulit-input NANDs and NORs are easily implemented in a CMOS circuit)

13. Logisim Circuit Software
Build digital circuits
Download:
Installed in classroom
100% Free
We will only use an extremely small subset of functionality available.
Basic logic gates
Inputs
Others
See Logisim PowerPoints for more info