15068_chapter4(Lect 41-44 Micro Operations)

8/8/2019 15068_chapter4(Lect 41-44 Micro Operations)

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cpe 252: Computer Organization 1

Register Transfer and Microoperations

Chapter 4:


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4-4 Arithmetic Microoperations

The microoperations most often

encountered in digital computers are

classified into four categories: Register transfer microoperations

Arithmetic microoperations (on numeric data

stored in the registers)

Logic microoperations (bit manipulations onnon-numeric data)

Shift microoperations


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The basic arithmetic microoperations are:

addition, subtraction, increment,

decrement, and shift Addition Microoperation:

R3 R1+R2

Subtraction Microoperation:R3 R1-R2 or :

R3 R1+R2+1

4-4 Arithmetic Microoperations cont.

1s complement


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Ones Complement Microoperation:

R2 R2

Twos Complement Microoperation:R2 R2+1

Increment Microoperation:

R2 R2+1 Decrement Microoperation:

R2 R2-1

4-4 Arithmetic Microoperations cont.


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Half Adder/Full AdderHalfAdder

0 0 0 0 0

0 0 1 0 10 1 0 0 10 1 1 1 01 0 0 0 11 0 1 1 01 1 0 1 01 1 1 1 1

cn = xy + xcn-1+ ycn-1= xy + (x y)cn-1

s = xycn-1+xycn-1+xycn-1+xycn-1= x y cn-1 = (x y) cn-1

x

y

cn-1x

y

cn-1

cn s

c = xy s = xy + xy

= x y

x

yc

s

xy

cn-1

S

cn

Full Adder

0 0 0 00 1 0 11 0 0 11 1 1 0

x y c s

x y cn-1 cn s0

01

0

0

11

1

0

10

1

1

01

0


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Binary Adder

FAFAFAFA C0

A0B0

S0

A1B1

S1

A2B2

S2

A3B3

S3

C1C2C3

C4

4-bit binary adder

(connection ofFAs)


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Binary Adder-Subtractor

FAFAFAFAC0

A0B0

S0

A1B1

S1

A2B2

S2

A3B3

S3

C1C2C3

C4

4-bit adder-subtractor

M


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For unsigned numbers, this gives A B if AB or

the 2s complement of (B A) if A < B

(example: 3 5 = -2= 1110)

For signed numbers, the result is A B provided

that there is no overflow. (example : -3 5= -8)1101

1011 +

1000



C3

C4V =

1, if overflow

0, if no overflow

Overflow detectorfor signed numbers


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cont.

What is the range of unsigned numbers

that can be represented in 4 bits?

What is the range of signed numbers thatcan be represented in 4 bits?

Repeat for n-bit?!


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Binary Incrementer

C S

x y

HA

C S

x y

HA

C S

x y

HA

C S

x y

HA

S0S1S2S3C4

1A0A1A2A3

4-bit Binary Incrementer


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Binary Incrementer Binary Incrementer can also be

implemented using a counter

A binary decrementer can be implementedby adding 1111 to the desired register

each time!


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Arithmetic Circuit This circuit performs seven distinct

arithmetic operations and the basic

component of it is the parallel adder

The output of the binary adder is

calculated from the following arithmetic

sum: D = A + Y + Cin


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B0


Arithmetic Circuit

cont.

3 2 1 0 S1 S0

41 MUX

FAFAFAFA Cin

D0D1D2D3

C1C2C3

Cout

B01 0 S1 S0B1

3 2 1 0 S1 S0

41 MUX

B11 0 S1 S0B2

3 2 1 0 S1 S0

41 MUX

B21 0 S1 S0B3

3 2 1 0 S1 S0

41 MUX

B31 0 S1 S0

A0A1A2A3

4-bit Arithmetic Circuit

X0Y0X1Y1X2Y2X3Y3

Figure A


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4-5 Logic Microoperations

The four basic microoperationsOR Microoperation

Symbol: , +

Gate:

Example: 1001102 10101102 = 11101102

P+Q: R1R2+R3, R4R5 R6

OROR

ADD


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The four basic microoperations

cont.AND Microoperation

Symbol:

Gate:

Example: 1001102 10101102 = 00001102


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cont.Complement (NOT) Microoperation

Symbol:

Gate:

Example: 10101102 = 01010012


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cont.XOR (Exclusive-OR) Microoperation

Symbol:

Gate:

Example: 1001102 10101102 =11100002


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Other Logic MicrooperationsSelective-set Operation

Used to force selected bits of a register

into logic-1 by using the OR operation

Example: 01002 10002 = 11002

In a processor registerLoaded into a register from

memory to perform the

selective-set operation


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Other Logic Microoperations

cont.

Selective-complement (toggling) Operation

Used to force selected bits of a register to be

complemented by using the XOR operation

Example: 00012 10002 = 10012

In a processor registerLoaded into a register from

memory to perform the

selective-complement operation


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Other Logic Microoperations cont.

Insert Operation

Step1: mask the desired bits

Step2: OR them with the desired value

Example: suppose R1 = 0110 1010, and wedesire to replace the leftmost 4 bits (0110) with1001 then:

Step1: 0110 1010 0000 1111

Step2: 0000 1010 1001 0000

R1 = 1001 1010


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Other Logic Microoperationscont.

NAND Microoperation

Symbols: and

Gate:

Example: 1001102 10101102 = 11110012


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NOR Microoperation

Symbols: and

Gate:

Example: 1001102 10101102 = 00010012


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Set (Preset) Microoperation

Force all bits into 1s by ORing them with a value

in which all its bits are being assigned to logic-1

Example: 1001102 1111112 = 1111112

Clear (Reset) Microoperation

Force all bits into 0s by ANDing them with a

value in which all its bits are being assigned tologic-0

Example: 1001102 0000002 = 0000002


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Hardware Implementation

The hardware implementation of logic

microoperations requires that logic gates

be inserted for each bit or pair of bits in the

registers to perform the required logic

function

Most computers use only four (AND, OR,

XOR, and NOT) from which all others canbe derived.


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Hardware Implementation cont.

S1S0

0

1

2

3

41

MUX

Ei

Ai

Bi

S1 S0 Output

Operatio

n

0 0 E = A B XOR

0 1 E = A B OR

1 0 E = A B AND

1 1 E = A Complement

This is for one bit i

Figure B


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4-6 Shift Microoperations

Used for serial transfer of data Also used in conjunction with arithmetic, logic,

and other data-processing operations

The contents of the register can be shifted to the

left or to the right

As being shifted, the first flip-flop receives its

binary information from the serial input

Three types of shift: Logical, Circular, andArithmetic


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4-6 Shift Microoperations cont.

r0r1r3rn-1

r0r1r2r3rn-1

Shift Right

Shift Left

Serial Input Serial Output

Serial Output Serial Input

Determines

the shift

type

r2

**Note that the bit ri is the bit at position (i) of the register


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4-6 Shift Microoperations:

Logical Shifts

Transfers 0 through the serial input

Logical Shift Right: R1shr R1

Logical Shift Left: R2shl R2

The same

The same

Logical Shift Left

? 0r0r1r2r3rn-1


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4-6 Shift Microoperations:Circular Shifts (Rotate Operation)

Circulates the bits of the register around

the two ends without loss of information

Circular Shift Right: R1cir R1

Circular Shift Left: R2cil R2

The same

The same

Circular Shift Left

r0r1r2r3rn-1


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Arithmetic Shifts

Shifts a signed binary number to the left or right

An arithmetic shift-left multiplies a signed binary

number by 2: ashl (00100): 01000

An arithmetic shift-right divides the number by 2

ashr (00100) : 00010

An overflow may occur in arithmetic shift-left,

and occurs when the sign bit is changed (signreversal)


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Arithmetic Shifts cont.

Arithmetic Shift RightSignBit

Arithmetic Shift LeftSignBit

?

0?

r0r1r2r3rn-1

r0r1r2r3rn-1


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Arithmetic Shifts cont.

An overflow flip-flop Vs can be used to

detect an arithmetic shift-left overflow

Vs = Rn-1 Rn-2

Rn-2Vs=

Rn-1 1 overflow

0 no overflow


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4-6 Shift Microoperations cont.

Example: Assume R1=11001110, then:

Arithmetic shift right once : R1 = 11100111

Arithmetic shift right twice : R1 = 11110011

Arithmetic shift left once : R1 = 10011100

Arithmetic shift left twice : R1 = 00111000

Logical shift right once : R1 = 01100111

Logical shift left once : R1 = 10011100

Circular shift right once : R1 = 01100111

Circular shift left once : R1 = 10011101


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A possible choice for a shift unit would be

a bidirectional shift register with parallel

load (refer to Fig 2-9). Has drawbacks:

Needs two pulses (the clock and the shift

signal pulse)

Not efficient in a processor unit where multiple

number of registers share a common bus It is more efficient to implement the shift

operation with a combinational circuit


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S 1 0 S 1 0 S 1 0 S 1 0

A3A2A1A0

Serial Input IR Serial Input IL

Select

0 for shift right

1 for shift left

H3 H2 H1 H0

MUX MUX MUX MUX

4-bit Combinational Circuit Shifter


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4-7 Arithmetic Logic Shift Unit

Instead of having individual registers

performing the microoperations directly,

computer systems employ a number of

storage registers connected to a common

operational unit called an Arithmetic Logic

Unit (ALU)


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4-7 Arithmetic Logic Shift Unit cont.

01

2

3

S3S2S1S0

BiAi

Ai+1Ai-1

Select

41

MUX

Ci

Ci+1

One stage ofarithmetic

circuit (Fig.A)

One stage of

logic circuit(Fig.B)

Di

Ei

Fi

shr

shl

One stage of

ALU

15068_chapter4(Lect 41-44 Micro Operations)

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