Lec13 Shifter

8/9/2019 Lec13 Shifter

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ECE2030Introduction to Computer Engineering

Lecture 13: Building Blocks forCombinational Logic (4 !"ifters#$ultipliers

Prof. Hsien-Hsin Sean LeeProf. Hsien-Hsin Sean Lee

School of Electrical and Computer EngineeringSchool of Electrical and Computer Engineering

Georgia TechGeorgia Tech


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Basic !"ifting

% !"ift directions& Left (multipl' b' 2

& ig"t (di)ide b' 2%*ake +oor )alue if t"e result is not an integer

%,loor )alue of -- (or - is t"e greatestinteger number less t"an or e.ual to -#-# E/g/ 2 2

32 2

% !"ift t'pes& Logical (or unsigned& rit"metic (or signed


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Logical !"ift

% !"ift Left& $!B: !"ifted out

& L!B: !"ifted in 5it" a 607

& E8amples:

% (11001011 99 1 10010110% (11001011 99 3 01011000

% !"ift rig"t

& $!B: !"ifted in 5it" a 607

& L!B: !"ifted out

& E8amples: (!ome I! use triple 67 for logical rig"ts"ift

% (11001011 1 01100101

% (11001011 3 00011001


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E8amples of rit"metic !"ift 1111 1011 rit"metic s"ift rig"tb' 1

1111 1101

1111 1011 rit"metic s"ift leftb' 1

1111 0110

1011 1111 ( > rit"metic s"ift leftb' 1 (i/e/ 82

0111 1110 ( ?12> 130 > rit"metic s"ift leftb' 1 (i/e/ 82

1000 0100 ( 124 ?132 @)er+o5 ;

@)er+o5


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4bit Logical !"ifter

!1 !0 A3 A2 A1 A0

0 - 3 2 1 0

1 0 0 3 2 1

1 1 2 1 0 0

3 2 1 0

A3 A2 A1 A0

!!

!0

!1

L

101010

001201111

101301212

201313

ASSASD

ASSASSASD

ASSASSASD

ASSASD

+=

++=

++=

+=


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4bit Logical !"ifter using 4to1 $u8

4to1 $u8

00 01 10 11s1

s0

!1 !0 A3 A2 A1 A0

0 - 3 2 1 0

1 0 0 3 2 1

1 1 2 1 0 0

A3

23

4to1 $u8

00 01 10 11s1

s0

A2

1

4to1 $u8

00 01 10 11s1

s0

A1

0

4to1 $u8

00 01 10 11s1

s0

A0

!1

!0

ig"t !"ift

Left !"ift


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4bit rit"metic !"ifter 5 4to1 $u8

4to1 $u8

00 01 10 11s1

s0

!1 !0 A3 A2 A1 A0

0 - 3 2 1 0

1 0 33 3 2 1

1 1 2 1 0 0

A3

23

4to1 $u8

00 01 10 11s1

s0

A2

1

4to1 $u8

00 01 10 11s1

s0

A1

0

4to1 $u8

00 01 10 11s1

s0

A0

!1

!0

ig"t !"ift

Left !"ift


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4to1 $u8

00 01 10 11s1

s0

!1 !0 A3 A2 A1 A0

0 - 3 2 1 0

1 0 33 3 2 1

1 1 2 1 0 0

A3

23

4to1 $u8

00 01 10 11s1

s0

A2

1

4to1 $u8

00 01 10 11s1

s0

A1

0

4to1 $u8

00 01 10 11s1

s0

A0

!1

!0

ig"t !"ift

Left !"ift@)er+o5@)er+o5


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4to1 $u8

00 01 10 11s1

s0

!1 !0 A3 A2 A1 A0

0 - 3 2 1 0

1 0 33 3 2 1

1 1 2 1 0 0

A3

23

4to1 $u8

00 01 10 11s1

s0

A2

1

4to1 $u8

00 01 10 11s1

s0

A1

0

4to1 $u8

00 01 10 11s1

s0

A0

!1

!0

ig"t !"ift

Left !"ift@)er+o5@)er+o5


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otator

S1 S0 D3 D2 D1 D0

0 0 3 2 1 0

0 1 0 3 2 1

1 0 1 0 3 2

1 1 2 1 0 3

4to1 $u8

00 01 10 11

s1s0

A3

23

4to1 $u8

00 01 10 11

s1s0

A2

1

4to1 $u8

00 01 10 11

s1s0

A1

0

4to1 $u8

00 01 10 11

s1s0

A0

!1

!0


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Barrel !"ifter

S2 S1 S0 D3 D2 D1 D00 0 0 3 2 1 0

0 0 1 3 3 2 1

0 1 0 3 3 3 2

0 1 1 3 3 3 3

1 0 0 3 2 1 0

1 0 1 2 1 0 0

1 1 0 1 0 0 0

1 1 1 0 0 0 0

!"ift multiple bitsmultiple bits at a time

Left !"ift

ig"t !"ift


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Barrel !"ifter Aesign 5 $u8 (A3

S2 S1 S0 D3

D2

D1

D0

0 0 0 3 2 1 0

0 0 1 3 3 2 1

0 1 0 3 3 3 2

0 1 1 3 3 3 3

1 0 0 3 2 1 0

1 0 1 2 1 0 0

1 1 0 1 0 0 0

1 1 1 0 0 0 0

4to1 $u8

00 01 10 11s1

s0

00 01 10 11s1s0

4to1 $u8

23to31$u8

23to31

$u8

1

0 A3

3

3 2 1 0

!0

!1

!2

eplicate and c"ange 5iring of t"e t5o 4to1 $u8es for A2# A1 an


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Barrel !"ifter Aesign lternati)e (1>bit

23!"ifter

22!"ifter

21!"ifter

20!"ifter

Leftig"t

!3

!2

!1

!0

1>

1>

1>

1>

(S3 S2 S1 S0) specifes the shit amount in binary(S3 S2 S1 S0) specifes the shit amount in binary

1>Output NumberOutput Number

Input NumberInput Number


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Barrel !"ifter Aesign 5 n$@!,E*

A3

A2

A1

A0

3

!0

(o !"ift

!1 !2 !3

2

1

0!3

!2

!1


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333


A3

A2

A1

A0

3

!0

(o !"ift

!1 !2!2 !3

2

1

0!3

!2!2

!1

3

2


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A3

A2

A1

A0

3

!0

(o !"ift

!1!1 !2 !3

2

1

0!3

!2

!1!1

3

3

2

1


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4bit D

a0 b0

CinCout

!um

B

!u"" #$$er!u"" #$$er

a0b0


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Dropagation Aela'

a0 b0

D0

a1 b0

a0 b1

0

D1

a2 b0

a1 b1

a0 b2

0

D2

a3 b0

a2 b1

a1 b2

a0 b3

0

D3

a3 b1

a2 b2

a1 b3

0

D4

a3 b2

a2 b3

D

a3 b3

D>D

1122

33

33

44

44

>>

>>==

484Aela' = adders

=8=Aela' 20 adder


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Dropagation Aela' of Carr'!a)e $ultiplier

a0 b0

D0

a3 b1

a2 b2

a1 b3

a3 b2

a2 b3

D

a3 b3

D

a1 b0

a0 b1

0

D1

11

22

33 33

>>

484

Aela' > adders

=8=Aela' 14 adders

a2 b0

a1 b1

a0 b2

0

D2

11

22

a3 b0

a2 b1

a1 b2

a0 b3

0

D3

11

22

33

440

D> D4


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!igned Binar' $ultipl'

F"en t"e $ultiplicand is negati)eF"en t"e $ultiplicand is negati)e

11101 (-3)

01001 (+9)

--------------------

11111101

00

11101

-------------------- 11100101

$aintain t"e sign bits of t"epartial product


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F"en t"e $ultiplier is negati)eF"en t"e $ultiplier is negati)e

01001 (+9)

11101 (-3)

--------------------

01001 01001

--------------------

0101101

01001

--------------------

01110101

10111

--------------------

111100101 (-27)

t t"e last step# 2Gscomplement t"e multiplicandbefore adding


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F"en bot" t"e $ultiplicand and $ultiplier are negatF"en bot" t"e $ultiplicand and $ultiplier are negat

10111 (-9)

11101 (-3)

--------------------

1110111 10111

--------------------

11010011

10111

--------------------

110001011

01001

--------------------

000011011(+27)

t t"e last step# 2Gscomplement t"e multiplicandbefore adding

$aintain t"e sign bits of t"epartial product


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$ore E8amples (1

1111 1010 (-6)

0000 0101 (+5)

--------------------

111111 1010

111110 10

--------------------

1110 0010 (-30)

ssume =bit numbers


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$ore E8amples (2

0011 (+3)

1110 (-2)

--------------------

0 0110

00 11

--------------------

01 0010

110 1

-------------------- 1010 (-6)

ssume 4bit numbers


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$ore E8amples (3

1111 1100 (-4)

1110 0000 (-32)

--------------------

111111 1000 0000

11 1111 00

--------------------

111 1110 1000 0000

000 0010 0

-------------------- 000 0000 1000 0000 (+128)

ssume =bit numbers

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Lec13 Shifter