SLIDE 1
Pirouz Bazargan Sabet February 2010 Digital Design
Pirouz Bazargan Sabet February 2010 Digital Design
Adders
Adding two natural numbers
- Let consider two natural numbers
- and
- coded on 8 bits using Natural Binary Code
Outline Digital CMOS design Arithmetic operators Adders Adders - - PowerPoint PPT Presentation
Outline Digital CMOS design Arithmetic operators Adders Adders - - PowerPoint PPT Presentation
Outline Digital CMOS design Arithmetic operators Adders Adders Comparators Shifters Multipliers Pirouz Bazargan Sabet Digital Design February 2010 Adders Adding two natural numbers Let consider two natural numbers and
SLIDE 2
SLIDE 3
Pirouz Bazargan Sabet February 2010 Digital Design
Adders
At each stage, I need to sum 3 single bit numbers
- The carry out of the stage i is the input carry of the next stage
- and
- are Boolean
functions of
- Adding two natural numbers
SLIDE 4
Pirouz Bazargan Sabet February 2010 Digital Design
00 01 11 10 1
- Adders
- 00
01 11 10 1
- ⊕
⊕ ⊕ ⊕
- ⊕
⊕ ⊕ ⊕
- +
+ + +
- +
+ + +
- Adding two natural numbers
SLIDE 5
Pirouz Bazargan Sabet February 2010 Digital Design
- Adders
- ⊕
⊕ ⊕ ⊕
- ⊕
⊕ ⊕ ⊕
- +
+ + +
- +
+ + +
- (
- +
+ + +
- )
- Adding two natural numbers
Addition delay depends on the delay of
- to
SLIDE 6
Pirouz Bazargan Sabet February 2010 Digital Design
- (
- +
+ + +
- )
- Adders
- ⊕
⊕ ⊕ ⊕
- ⊕
⊕ ⊕ ⊕
- +
+ + +
- +
+ + +
- +
+ + + (
- )
- Adding two natural numbers
SLIDE 7
Pirouz Bazargan Sabet February 2010 Digital Design
- Adders
- +
+ + + (
- ⊕
⊕ ⊕ ⊕
- )
- Adding two natural numbers
- ⊕
⊕ ⊕ ⊕
- ⊕
⊕ ⊕ ⊕
- +
+ + +
- +
+ + +
- +
+ + + (
- )
SLIDE 8
Pirouz Bazargan Sabet February 2010 Digital Design
- Adders
- Adding two natural numbers
The circuit generating
- and
- is called a Full Adder (FA)
SLIDE 9
Pirouz Bazargan Sabet February 2010 Digital Design
Adders
At each stage, I need to sum 3 single bit numbers
- The carry out of the stage i is the input carry of the next stage
Adding two natural numbers
Ripple Carry Adder (RCA)
FA
- FA
- FA
- FA
SLIDE 10
Pirouz Bazargan Sabet February 2010 Digital Design
Adders
Adding two natural numbers
Ripple Carry Adder (RCA)
FA
- FA
- FA
- FA
- Area ∝ n
Delay ∝ n Timing should be improved
SLIDE 11
Pirouz Bazargan Sabet February 2010 Digital Design
Adders
Adding two natural numbers
Acceleration technics
Adder
- Adder
- either 0 or 1
- Adder
- Carry Select Adder (CSLA)
SLIDE 12
Pirouz Bazargan Sabet February 2010 Digital Design
Adders
Adding two natural numbers
Carry Select Adder (CSLA)
- FA
- FA
- Area ∝ nlog(3) = n1.585
Delay ∝ log (n)
SLIDE 13
Pirouz Bazargan Sabet February 2010 Digital Design
Adders
00 01 11 10 1
- Adding two natural numbers
Acceleration technics
carry out does not depend on carry in carry out depends
- n carry in
- 00
01 11 10
generation absorption propagation propagation
SLIDE 14
Pirouz Bazargan Sabet February 2010 Digital Design
Adders
Adding two natural numbers
Acceleration technics
- 00
01 11 10
generation absorption propagation propagation
- ⊕
⊕ ⊕ ⊕
- ⊕
⊕ ⊕ ⊕
- 00
01 11 10 1
SLIDE 15
Pirouz Bazargan Sabet February 2010 Digital Design
Adders
Adding two natural numbers
Acceleration technics
- 00
01 11 10
generation absorption propagation propagation
- ⊕
⊕ ⊕ ⊕
- ⊕
⊕ ⊕ ⊕
SLIDE 16
Pirouz Bazargan Sabet February 2010 Digital Design
Adders
Adding two natural numbers
Acceleration technics
SLIDE 17
Pirouz Bazargan Sabet February 2010 Digital Design
Adders
Adding two natural numbers
Acceleration technics
- ⊕
⊕ ⊕ ⊕
- ⊕
⊕ ⊕ ⊕
- .
. . .
- +
- .
. . .
SLIDE 18
Pirouz Bazargan Sabet February 2010 Digital Design
- Adders
SLIDE 19
Pirouz Bazargan Sabet February 2010 Digital Design
Adders
Slansky Adder
SLIDE 20
Pirouz Bazargan Sabet February 2010 Digital Design
Adders
Kogge-Stone Adder
SLIDE 21
Pirouz Bazargan Sabet February 2010 Digital Design