rt level combinational blocks paolo prinetto politecnico di torino (italy) university of illinois at...

RT level RT level combinational combinational

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RT level RT level combinational combinational

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Paolo PRINETTOPolitecnico di Torino (Italy)

University of Illinois at Chicago, IL (USA)

[email protected] [email protected]

www.testgroup.polito.it

Lecture

5.1

2 5.1

Goal

This lecture presents the set of functional blocks that are usually considered to be “elementary” or “basic” at the RT level.

3 5.1

Prerequisites

Lecture 3.3

4 5.1

Homework

No particular homework is foreseen

5 5.1

Further readings

Students interested in making a reference to a text book on the arguments covered in this lecture can refer, for instance, to:

M. Morris Mano, C.R.Kime: “Logic and Computer Design Fundamentals,” 2nd edition updatedPrentice Hall, Upple Saddle River, NJ (USA), 2001, (chapter 3, pp. 111-148 )

6 5.1

Elementary functional blocksElementary functional blocks

MultiplexerMultiplexer

Adder-Adder-SubtracterSubtracter DecoderDecoder

EncoderEncoder

ComparatorComparatorROMROM

ALUALU

MultiplierMultiplier

1’s counter1’s counterI/O interfacesI/O interfaces

7 5.1

AddersAdders

We shall consider:

half adder

full adder

adder-subtracter

8 5.1

Half-Adder

A half-adder has:

2 inputs Ai, Bi

2 outputs Si and Ci+1

and computes the binary sum of the 2 input bits, providing:

the sum Si

the carry Ci+1

9 5.1

Si = Ai Bi

Ci+1 = Ai Bi

AAii B Bii

CCi+1 i+1 SSii

10 5.1

Full-Adder

A full-adder has:

3 inputs Ai, Bi and Ci

2 outputs Si and Ci+1

and computes the binary sum of the 3 input bits, providing:

the sum Si

the carry Ci+1

11 5.1

Si = Ai Bi Ci

Ci+1 = Ai Bi + Ai Ci + Bi Ci =

= Ai Bi + ( Ai Bi ) Ci

AAii B Bi i CCii

CCi+1 i+1 SSii

12 5.1

Adder-subtracterAdder-subtracter

An adder-subtracter is a combinational block capable of adding/subtracting two n-bits inputs operands, detecting overflow conditions. It has

2 n-bits data inputs, both labeled from n-1 to 0

1 control input to select one of the two operations

1 n-bits data output

1 control output asserted when an overflow condition is occurred.

13 5.1

Adder-subtracter Adder-subtracter (cont’d)

FUNC(n-1 downto 0)

A(n-1 downto 0)

B(n-1 downto 0)

ADD/~SUB

OVFL

Symbol

14 5.1



EncoderEncoder


ALUALU




15 5.1


A multiplexer is a combinational block capable of forcing its output to the current value of one of its inputs, according to the values of some control signals.

Each input can be either a single wire or a bus.

16 5.1


A multiplexer has:

2k data inputs, labeled from 2k-1 to 0

k control inputs

1 data output.

k 22kk-1 2-1 2kk-2 2 1 0-2 2 1 0MUXMUX

…

It gets the value It gets the value present on the input present on the input

labeled labeled 2 2 ii, where, where i i ((0 0 i i k-1k-1) is the ) is the

binary number present binary number present on the control inputs.on the control inputs.

17 5.1

OUT

SEL(k-1 downto 0)

Multiplexer (cont'd)

Symbol

IN(2k-1 downto 0)

18 5.1

Multiplexer (cont’d)

Symbol

M0(n-1 downto 0)

OUT(n-1 downto 0)

M1(n-1 downto 0)

M2(n-1 downto 0)

M2k-1(n-1 downto 0)

SEL(k-1 downto 0)

19 5.1




EncoderEncoder


ALUALU



20 5.1

DecoderDecoder

A decoder k 2k has:

1 n-bit data input

2 n outputs, labeled from 0 to 2 n-1

1 enable.

When enabled, just the output labeled 2 j is active, where j is the value present on the data input.

When disabled, no output is active.

21 5.1

Decoder (cont’d)

SymbolDOUT(0)

DIN(n-1 downto 0)

ENABLE

DOUT(1)

DOUT(2)

DOUT(2n-1)

22 5.1




EncoderEncoder


ALUALU



23 5.1

Priority EncoderPriority Encoder

A priority encoder has:

2k inputs, labeled from 0 to 2k-1 (each input is assigned a fixed priority)

k outputs

1 “data valid” output

1 enable.

24 5.1

Priority Encoder Priority Encoder (cont’d)(cont’d)

When enabled:

the outputs get the value j , where j is the label of the highest priority asserted input

the “data valid” output is asserted.

When disabled or when no input is asserted:

the “data valid” output is not asserted.

25 5.1

M0

CODE(n-1 downto 0)

ENABLE

M1

M2

M2n-1

Priority Encoder (cont’d)

VALID

Symbol

26 5.1




EncoderEncoder


ALUALU



27 5.1

ComparatorComparator

A comparator gets 2 n-bit binary numbers:

A(n-1 downto 0) B(n-1 downto 0)

and provides in output the result of the comparison between A and B.

A control input UM/~2C specifies whether the input operands are unsigned or signed, respectively.

28 5.1

Comparator (cont’d)

AA

BB

AeqBAeqB

AneBAneB

AltBAltB

AgtBAgtB

AleBAleB

AgeBAgeB

Symbol

B(n-1 downto 0)

A(n-1 downto 0)

UM/~2CSel

29 5.1




EncoderEncoder


ALUALU



30 5.1

Counter of 1’s occurrencesCounter of 1’s occurrences

A counter of 1’s occurrences has:

1 n-bit data input

1 m-bit data output, being m = log2 n .

The device counts the number of occurrences of a ‘1’ on its inputs and provides it on its outputs.

31 5.1

Counter of 1’s occurrencesCounter of 1’s occurrences(cont’d)

Symbol

DIN(n-1 downto 0)1’s C1’s C

DOUT(m-1 downto 0)

32 5.1




EncoderEncoder


ALUALU



33 5.1

ROMROM

A 2k n ROM (Read-Only Memory) has:

k address inputs

n data outputs

2k n-bit internal cells, storing permanent values.

The outputs gets the value stored in the j cell, j being the current value present on address inputs.

34 5.1

ROM (cont’d)

ADDRADDR

D_OUTD_OUT

Symbol

ADDR(2k-1 downto 0)

DATA(n-1 downto 0)

35 5.1




EncoderEncoder


ALUALU



36 5.1

ALUALU

An n-bit ALU (Arithmetic Logic Unit) performs logic and/or arithmetic operations on 2 n-bit operands, under the control of ad-hoc control signals.

37 5.1

ALU (cont’d)

FUNC(n-1 downto 0)

CONTROL

C_IN

C_OUT

STATUS

Symbol

B(n-1 downto 0)

A(n-1 downto 0)

38 5.1

F=A B

F=A B'

Functions implemented by the ALU ’181

Input Functions

S3 S2 S1 S0 arithmetic (M=0) logic (M=1)

0 0 0 00 0 0 10 0 1 00 0 10 1 0 00 1 0 10 1 1 0

1

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

F=A minus 1 plus CINF=AB minus 1 plus CINF=AB' minus 1 plus CINF=1111 plus CINF=A plus (A+B') plus CINF=AB plus (A+B') plus CINF=A minus B minus 1 plus CINF=A+B' plus CINF=A plus (A+B) plus CINF=A plus B plus CINF=AB' plus (A+B) plus CINF=A+B plus CINF=A plus A plus CINF=AB plus A plus CINF=AB' plus A plus CINF=A plus CIN

F=A'F=A'+ B'F=A'+ BF= 1111F=A'B'F=B'

F=A+B'F=A'B

F=BF=A+BF=0000F=AB'F=ABF=A

39 5.1




EncoderEncoder


ALUALU



40 5.1


A multiplier has:

1 n-bits data inputs, labeled from n-1 to 0

1 m-bits data inputs, labeled from m-1 to 0

no control signals

k-bits data outputs, labeled from k-1 to 0

and provides in output the results of the product between the two input operands.

41 5.1

Multiplier Multiplier (cont’d)(cont’d)

MUL_OUT(k-1 downto 0)*

B(n-1 downto 0)

A(m-1 downto 0)

Symbol

42 5.1

Multiplier Multiplier (cont’d)(cont’d)

MUL_OUT(k-1 downto 0)*

B(n-1 downto 0)

A(m-1 downto 0)

Symbol • Signed operands: Signed operands: k=m+n-1k=m+n-1

• Unsigned operands: Unsigned operands: k=m+nk=m+n

43 5.1




EncoderEncoder


ALUALU



44 5.1

I/O interfacesI/O interfaces

The combinational interfaces for the following I/O devices will be presented:

led bar driver

7-segments display

dip-switch

keypad.

45 5.1

Led bar interface

LED_BAR LED_BAR interfaceinterface

n

DATA(n-1 downto 0)

46 5.1

DATA

DISPLAYDISPLAYinterfaceinterface

4, 7

DOT

ENABLE

7-segments display interface

47 5.1

a

b

c

d

e

f

g

BIBI

AABBCCDD

aabbccddeeffgg

abcdefg

DOT

ENABLE

7-segments display interface

48 5.1

Dip-switch interface

DATADIP_SWDIP_SWinterfaceinterface n

n

49 5.1

Keypad interface

DATA

KEYPADKEYPADinterfaceinterface

4, 7

00 11 22 33

44 55 66 77

88 99 AA BB

CC DD EE FFDATA_VALID

rt level combinational blocks paolo prinetto politecnico di torino (italy) university of illinois at...

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