Digital Logic Gates

Sum of Products (Review)

Procedure:1. Form a minterm for each combination of the variables that produces a 12. OR all the minterms.

Three-Terminal AND Gate

F2 A B C

0 0 0 0

0 0 0 1

0 0 1 0

0 0 1 1

0 1 0 0

0 1 0 1

0 1 1 0

1 1 1 1

𝑓 1=𝐴 ∙𝐵 ∙𝐶=( 𝐴 ∙𝐵 ) ∙𝐶=𝐴 ∙ (𝐵 ∙𝐶 )=𝐴 ∙𝐵 ∙𝐵 ∙𝐶=( 𝐴 ∙𝐵 ) ∙ (𝐵 ∙𝐶 )

Application of Sum of Products

𝑓 1=𝐴 ∙𝐵 ∙𝐶=( 𝐴 ∙𝐵 ) ∙𝐶=𝐴 ∙ (𝐵 ∙𝐶 )=𝐴 ∙𝐵 ∙𝐵 ∙𝐶=( 𝐴 ∙𝐵 ) ∙ (𝐵 ∙𝐶 )

Digital Logic Gates

2-Input AND GateNAND INV

NAND INV

2-Input OR Gate

NOR INV

NOR INV

Universal Gates

• NAND and NOR are easier to build than AND and OR

• NAND and NOR are used to implement AND and OR gates

NAND/NOR

NAND-Based OR Gate

NOR-Based NAND Gate

XOR/XNOR

F=1 when x≠y

F=1 when x=y

Application of an XOR Gate

Use a XOR to Generate Pseudo-Random Numbers

Reference: http://en.wikipedia.org/wiki/Linear_feedback_shift_register

logic.ly/demo

Circuit Simplification Example

Solution

Factoring—the first & third terms above haveAC in common, which can be factored out:

Since B + B = 1, then…

z = A(C + B)

Topics for Quiz 1

• Date: 3/8/2012– In class– No Make-Up

• Number Conversion• Arithmetic Operations• Complements• Signed Binary Numbers• Addition/Subtraction• Boolean Algebra• Logic Gates• Sum of Products• Circuit Simplifications

Example 1

Example 2