lecture 4

240-451 VLSI lecture, 2000

Lecture 4Lecture 4

MOS Circuits

Department of Computer Engineering, Prince of Songkla University by Wannarat Suntiamorntut

240-451 VLSI lecture, 2000

Department of Computer Engineering, Prince of Songkla University by Wannarat Suntiamorntut

Combination & Sequential

Logic

Circuit

Logic

CircuitOut

OutInIn

(a) Combinational (b) Sequential

State

Output = f(In) Output = f(In, Previous In)

240-451 VLSI lecture, 2000

Department of Computer Engineering, Prince of Songkla University by Wannarat Suntiamorntut

Combination & Sequential

240-451 VLSI lecture, 2000

Department of Computer Engineering, Prince of Songkla University by Wannarat Suntiamorntut

CMOS logic style

240-451 VLSI lecture, 2000

Department of Computer Engineering, Prince of Songkla University by Wannarat Suntiamorntut

Example NAND gate

240-451 VLSI lecture, 2000

Department of Computer Engineering, Prince of Songkla University by Wannarat Suntiamorntut

4-input NAND gate

Out

In1 In2 In3 In4

In3

In1

In2

In4

In1 In2 In3 In4

VDD

Out

GND

VDD

240-451 VLSI lecture, 2000

Department of Computer Engineering, Prince of Songkla University by Wannarat Suntiamorntut

Example : NOR gate

240-451 VLSI lecture, 2000

Department of Computer Engineering, Prince of Songkla University by Wannarat Suntiamorntut

Complex CMOS gate

240-451 VLSI lecture, 2000

Department of Computer Engineering, Prince of Songkla University by Wannarat Suntiamorntut

Complex gate structures

A

C

B

A

B C

Vdd

Gnd

OutOut = A+(B*C) ...

ABC

And-Or-Invert (AOI)

How to add terms?

240-451 VLSI lecture, 2000

Department of Computer Engineering, Prince of Songkla University by Wannarat Suntiamorntut

A

C

B

A

B C

Vdd

Gnd

OutOut = A+(B*C) ...

ABC

And-Or-Invert (AOI)

How to add terms?

OAI/AOI duality

240-451 VLSI lecture, 2000

Department of Computer Engineering, Prince of Songkla University by Wannarat Suntiamorntut

Demorgan’s law in action

Out = A*(B+C) ...

ABC

Or-And-Invert (OAI)

A

C

B

A

B

C

Vdd

Gnd

Out

240-451 VLSI lecture, 2000

Department of Computer Engineering, Prince of Songkla University by Wannarat Suntiamorntut

Demorgan’s law in action

Out = A*(B+C) ...

ABC

Or-And-Invert (OAI)

A

C B A

BC

Vd

dGn

d

Ou

t

240-451 VLSI lecture, 2000

Department of Computer Engineering, Prince of Songkla University by Wannarat Suntiamorntut

Demorgan’s law in action

Out = A*(B+C) ...

ABC

Or-And-Invert (OAI)

A

C

B

A

B

C

Vdd

Gnd

Out

240-451 VLSI lecture, 2000

Department of Computer Engineering, Prince of Songkla University by Wannarat Suntiamorntut

Demorgan’s law in action

Out = A*(B+C) ...

ABC

Or-And-Invert (OAI)

A

C

B

A

BC

Vdd

Gnd

Out

240-451 VLSI lecture, 2000

Department of Computer Engineering, Prince of Songkla University by Wannarat Suntiamorntut

Demorgan’s law in action

Out = A*(B+C) ...

ABC

Or-And-Invert (OAI)

A

C

B

A

BC

Vdd

Gnd

Out

What is the Magic command to do this?

240-451 VLSI lecture, 2000

Department of Computer Engineering, Prince of Songkla University by Wannarat Suntiamorntut

OAI/AOI duality

B

A

C

OUT

A

C

B

A

B C

Vdd

Gnd

Out

A

B

C

OUT

A

C

B

A

BC

Vdd

Gnd

Out

240-451 VLSI lecture, 2000

Department of Computer Engineering, Prince of Songkla University by Wannarat Suntiamorntut

Step by step layout XNOR gate

• The equation for XNOR is:

– f = (a * b) + (a' * b')

• using DeMorgan's law on each of the two terms gives:

– f = (a'+ b')' + (a + b)'

• using DeMorgan's law on the two terms together gives:

– f = ((a'+ b') * (a + b))'

• This could be directly implemented with a single complementary CMOS gate: the equation is in a simple negated product of sums form. This form can be implemented with the standard Or-And-Invert (OAI) style gate.

240-451 VLSI lecture, 2000

Department of Computer Engineering, Prince of Songkla University by Wannarat Suntiamorntut

Non-inverter input

• However, using DeMorgan's law one more time on the left term gives:

– f = ((a * b)' * (a + b))’

• This form uses no inverted inputs and can be implemented with two gates a NAND gate and an OAI gate.

ab f

240-451 VLSI lecture, 2000

Department of Computer Engineering, Prince of Songkla University by Wannarat Suntiamorntut

Logic Graph

240-451 VLSI lecture, 2000

Department of Computer Engineering, Prince of Songkla University by Wannarat Suntiamorntut

Example CMOS

240-451 VLSI lecture, 2000

Department of Computer Engineering, Prince of Songkla University by Wannarat Suntiamorntut

Complex CMOS graph