Discrete Mathematics CS 2610

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# Discrete Mathematics CS 2610 - PowerPoint PPT Presentation

Discrete Mathematics CS 2610. February 19, 2009. X. X+Y. Y. Logic Gates: the basic elements of circuits. Electronic circuits consist of so-called gates connected by wires. x. x. Inverter (NOT gate ). OR gate. x. xy. AND gate. y. Multiway Logical Gates.

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### Discrete Mathematics CS 2610

February 19, 2009

X

X+Y

Y

Logic Gates: the basic elements of circuits
• Electronic circuits consist of so-called gates connected by wires

x

x

Inverter (NOT gate)

OR gate

x

xy

AND gate

y

Multiway Logical Gates
• Multiple Input AND, OR Gates

x1

x1+x2+… + xn

x2

xn

x1

x1x2…  xn

x2

xn

Combinational Circuits
• Combinational Circuits are circuits in which the logical gates’ outputs depend on their current inputs only
• No loops
• No memory capabilities
• No current state worries
Circuit Design
• Design a circuit for xy + xy

x

y

xy + xy

F

x

y

0

0

1

0

1

0

1

0

0

1

1

1

Circuit Design
• Design a circuit for xy + xy

x

y

xy + xy

F

x

y

0

0

0

0

1

1

1

0

1

1

1

0

Circuit Design: XOR

Design a circuit that implements the XOR (the stairway lighting problem)

xy + xy

x

y

xy + xy

Circuit Design (aside)

up

The stairway light switches:

down

up

Switch 2

down

up

Switch 1

down

+ -

Circuit Design
• Design a circuit for xy + z