Chapter 9 Sequential Circuit Design:...

Chapter 9

Sequential Circuit Design:

Practice

ECOM 4311

Digital System Design using VHDL

2

Outline

1. Poor design practice and remedy

2. More counters

3. Register as fast temporary storage

4. Pipelined circuit

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1. Poor design practice and remedy

Synchronous design is the most

important methodology

Poor practice in the past (to save chips)

• Misuse of asynchronous reset

• Misuse of gated clock

• Misuse of derived clock

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Misuse of asynchronous reset

• Poor design: use reset to clear register in normal operation.

• e.g., a poorly mod-10 counter

oClear register immediately after the counter reaches 1010

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Problem

• Glitches in transition 1001 (9) => 0000 (0)

• Glitches in aync_clr can reset the counter

• How about timing analysis? (maximal clock

rate)

Asynchronous reset should only be used

for power-on initialization

Remedy: load “0000” synchronously


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Remedy: load “0000” synchronously

Remedy

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Misuse of gated clock

• Poor design: use a and gate to disable the

clock to stop the register to get new value

• E.g., a counter with an enable signal

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Problem

• Gated clock width can be narrow

• Gated clock may pass glitches of en

• Difficult to design the clock distribution

network

Misuse of gated clock

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• Remedy: use a synchronous enable

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Misuse of derived clock

• Subsystems may run at different clock rate

• E.g., second and minutes counter

o Input: 1 MHz clock

o Poor design:

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o Better design

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2. More counters

• Counter circulates a set of specific patterns

• Counter: o Binary

o Gray counter

o Ring counter

o Linear Feedback Shift Register (LFSR)

o BCD counter

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o State follows binary counting sequence

oUse an incrementor for the next-state logic

d

clk

q

reset

+1r_reg r_next

reset

clk

q

Binary counter

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o State changes one-

bit at a time

oUse a Gray

incrementor

Gray counter:

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Gray counter:

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Gray counter:

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Gray counter:

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Ring counter

Circulate a single 1

E.g., 4-bit ring counter: 1000, 0100, 0010, 0001

n patterns for n-bit register

Non self-correcting design

• Insert “0001” at initialization and circulate the pattern in normal operation

• Fastest counter

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Ring counter

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Ring counter

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Ring counter

This simple design makes this a very fast counter (much faster than binary cnter)

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Self-correcting design:

A self-correcting design ensures that a ’1’ is

always circulating in the ring

This is accomplished by inspecting the 3 MSBs if

"000", then the combo. Logic inserts a ’1’ into the

low order bit

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LFSR (Linear Feedback Shift Reg)

An LFSR is a shifter register that contains

an XOR feedback network that determines

the next serial input value

Only a subset of the register bits are used

in the XOR operation

By carefully selecting the bits, an LFSR can

be designed to circulate through all 2n-1

states for an n-bit register

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• E.g, 4-bit LFSR

Note that the state "0000" is excluded -- if it ever shows up, the

LFSR becomes stuck

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Property of LFSR

• N-bit LFSR can cycle through 2n-1 states

• The feedback circuit to generate a maximal

number of states exists for any n

• The sequence is pseudorandom

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Application of LFSR

• Pseudorandom: used in testing, data

encryption/decryption

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4-bit LFSR

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4-bit LFSR

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4-bit LFSR

Read remaining of Section 9.2.3 (design to including

00..00 state)

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Decimal Counter

A decimal counter circulates the patterns

in binary-coded decimal (BCD) format. The

BCD

code uses 4 bits to represent a decimal

number. For example, the BCD code for

the three digit decimal number 139 is "0001

001 1 1001".

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Decimal Counter

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Decimal Counter

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Decimal Counter

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Decimal Counter

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PWM (pulse width modulation)

Duty cycle: percentage of time that the

signal is asserted

PWM: use a signal, w, to specify the duty

cycle

• Duty cycle is w/16 if w is not “0000”

• Duty cycle is 16/16 if w is “0000”

Implemented by a binary counter with a

special output circuit

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Register as fast temporary storage

RAM • RAM cell designed at transistor level

• Cell use minimal area

• Behave like a latch

• For mass storage

• Need a special interface logic

Register • D FF requires much larger area

• Synchronous

• For small, fast storage

• E.g., register file, fast FIFO, Fast CAM (content addressable memory)

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Register file

Registers arranged as an 1-d array

Each register is identified with an address

Normally has 1 write port (with write enable

signal)

Can has multiple read ports

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• E.g., 4-word register file with 1 write port

and two read ports

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Register array:

• 4 registers with 16 bits

• Each register has an enable signal

Write decoding circuit:

• 0000 if wr_en is 0

• 1 bit asserted according to w_addr if wr_en is 1

Read circuit:

• A mux for each read port

Register file

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VHDL Implementation code

A 2-D data type is needed here

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VHDL Implementation code

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FIFO Buffer

• “Elastic” storage between two subsystems

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Circular queue implementation

Use two pointers and a “generic storage”

• Write pointer: point to the empty slot before

the head of the queue

• Read pointer: point to the tail of the queue

FIFO Buffer

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FIFO Buffer

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FIFO controller

• Read and write pointers: 2 counters

• Status circuit:

• Difficult

• Design 1: Augmented binary counter

• Design 2: with status FFs

• LSFR as counter

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Augmented binary counter:

• increase the counter by 1 bits

• Use LSBs for as register address

• Use MSB to distinguish full or empty

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FIFO controller with Augmented counter

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FIFO controller with Augmented counter

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2 extra status FFs

• Full_erg/empty_reg memorize the current

staus

• Initialized as 0 and 1

• Modified according to wr and rd signals:

• 00: no change

• 11: advance read pointer/write pointer; full/empty

no change

• 10: advance write pointer; de-assert empty; assert

full if needed (when write pointer=read pointer)

• 01: advance read pointer; de-assert full; asserted

empty if needed (when write pointer=read pointer)

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2 extra status FFs

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Other design

Non-binary counter for the pointer

• Exact location does not matter as long as the

write pointer and read pointer follow the same

pattern

• Other counters can be used for the second

scheme

• E.g, use LFSR

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4. Pipelined circuit

• Two performance criteria:

o Delay: required time to complete one task

o Throughput: number of tasks completed per unit time.

• E.g., ATM machine

o Original: 3 minutes to process a transaction

delay: 3 min; throughput: 20 trans per hour

o Option 1: faster machine 1.5 min to process

delay: 1.5 min; throughput: 40 trans per hour

o Option 2: two machines

delay: 3 min; throughput: 40 trans per hour

• Pipelined circuit: increase throughput

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Pipeline: overlap certain operation

E.g., pipelined laundry:

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Pipeline

Non-pipelined:

• Delay: 60 min

• Throughput 1/60 load per min

Pipelined:

• Delay: 60 min

• Throughput k/(40+k*20) load per min

about 1/20 when k is large

• Throughput 3 times better than non-pipelined

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Pipelined combinational circuit

Basic idea is to divide the combinational logic into a set of

stages, with buffers (registers or latches) inserted

between each stage

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Given a pipeline with stage delays of T1, T2, T3 and T4,

clock cycle time is bounded by :

ADD the setup and clock-to-q delays of the pipeline

registers

In non-pipelined version, delay to process one item is

For the pipelined version, its actually longer

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The win is actually w.r.t. the throughput

metric

For pipelined version, it takes 3*Tc time to

fill the pipeline and the time to process k

items is 3*Tc + kTc yielding :

TP = k/(3*Tc + kTc)

which approaches 1/Tc for large k

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Adding pipeline to a comb circuit

• Not all circuits are amenable to pipelines.

• The following criteria required for pipelining:

oData is always available for the pipelined

circuit’s inputs

o System throughput is an important

performance characteristic

oCombinational circuit can be divided into

stages with similar propagation delays

o Propagation delay of a stage is much larger

than the Tsetup and Tcq of the register

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• Derive the block diagram of the original

combinational circuit and arrange the circuit as a

cascading chain

• Identify the major components and estimate the

relative propagation delays of these components

• Divide the chain into stages of similar

propagation delays

• Identify the signals that cross the boundary of

the chain

• Insert registers for these signals in the

boundary.

Procedure

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Pipelined comb multiplier

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The two major components are the adder

and bit-product generation circuit

Arrange this components in cascade as

shown on the next slide, with the bit-

product labeled as BP

The bit-product circuit is simply an AND

operation and therefore has a small delay

We combine it with the adder to define a

stage


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There are two types of pipeline registers

• One type to accommodate the computation

flow and to store the intermediate results

(partial products pp1, ... pp4)

• Second type to preserve the info needed in

each stage, i.e., a1, a2, a3, b1, b2, and b3

• Since there are different multiplications

occurring in each stage, the operands for any

given multiplication must move along with the

partial products

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Congratulation! Your first pipeline….

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