Chap 8. Sequencing and Control

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Chap 8. Sequencing and Control
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8.1 Introduction

• Binary information in a digital computer
• data
• manipulated in a datapath with ALUs, registers,
  multiplexers, and buses
• control
• provide signals that activate the various
  microoperations determine the sequence in which
  the various actions are performs
• Synchronous digital system
• Achieve synchronism by a master clock generator
• Control unit
• Generates binary variables that control the
  selection inputs of multiplexers, buses, ALUs,
  load control inputs of registers

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8.1 Introduction

• Control unit
• a sequential circuit with state that dictate the
  control signals for the system
• using status conditions and control inputs, the
  sequential control unit determines the next
  state, in which additional microoperations are
  activated
• 2 distinct types of control units
• For programmable system
• For nonprogrammable system

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8.1 Introduction

• Programmable system
• Input a sequence of instructions
• Instructions specify the operations the system is
  to perform
• instructions are stored in memory (RAM or ROM)
• program counter (PC)
• provide the address in memory of the instructions
  to be executed
• executing an instruction
• activating the necessary sequence of
  microoperations in the datapath that are
  required to perform the operation specified by
  the instruction
• Non-programmable system
• not responsible for obtaining instructions, nor
  for sequencing the execution of those
  instructions
• determines the operation to be performed the
  sequence of those operations, based on only its
  inputs and the status bits

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8.2 Algorithmic State Machines

• Data processing tasks
• register transfer operations controlled by a
  sequencing mechanism
• can be specified as a hardware algorithm that
  consists of a finite number of procedural steps
  which perform the data processing task
• Flowchart
• a convenient way to specify a sequence of
  procedural steps decision paths for an hardware
  algorithm
• ASM (Algorithmic State Machine)
• describes a sequence of events, as well as the
  timing relationship between the states actions
• Cf) S/W program S/W algorithm - Flowchart

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8.2 Algorithmic State Machines

• ASM Chart Elements
• state box register transfer operations or
  output signals
• decision box describes the effect of inputs on
  the control
• conditional output box from decision box

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8.2 Algorithmic State Machines

• ASM chart
• State diagram for the sequential circuit part of
  the control unit
• An ASM block
• One state block
• All of the decision and conditional output boxes
  connected between the state box exit and entry
  paths to the same or other state boxes.

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8.2 Algorithmic State Machines

• ASM Timing Consideration

0
1
Register transfers and state changes both wait
until the next positive clock edge.
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8.3 Decision Example Binary Multiplier

• multiplies 2 unsigned binary numbers

Binary Multiplier a copy of the multiplicand is
added to a partial product the partial product
is stored in a register for the shift action the
partial product is shifted to the right (adder
is needed for only n bit positions
instead of 2n bit)
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8.3 Decision Example Binary Multiplier

• Hardware Multiplication Example

n-bits
Partial product

Copy of multiplicand
Partial product stored in a register in
preparation for the shift action to follow
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8.3 Decision Example Binary Multiplier

• Block Diagram for Binary Multiplier

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8.3 Decision Example Binary Multiplier

• multiplicand is loaded into register B from IN
• multiplier is loaded into register Q from IN
• partial product is formed in reg A, stored in
  reg A Q
• C F/F stored the carry Cout shifted into
  the MSB of A,
• LSB of A is shifted into the MSB of Q, LSB
  of Q is discarded
• Q0 holds the bit of the multiplier that must be
  considered next
• counter P
• count the number of add-shift or shift actions
• initially set to n-1 counted down

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8.3 Decision Example Binary Multiplier

• ASM Chart for Multiplier
• IDLE
• multiplication process starts when G becomes 1
• (ASM moves from state IDLE to
  state MUL0)
• MUL0
• a decision is made based on Q0
• MUL1
• a right shift is performed on C, A, Q
• C ? 0, C ?? A ?? Q ? sr C ?? A ?? Q

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8.4 Hardwired Control

• 2 distinct aspects to deal with
• control of the microoperations
• part of the control that generates the control
  signals
• Table 8-1
• sequencing of the control unit microoperations
• part of the control that determines what happens
  next
• Table 8-2

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8.4 Hardwired Control

• Control signals for binary multiplier
• based on the ASM chart

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8.4 Hardwired Control

• Sequencing Part of ASM Chart
• information on sequencing is represented with
  information on microoperations removed
• conditional output boxes are removed
• decision box not affecting the next state is
  removed
• design the sequencing part of the control unit
  with the ASM chart i.e. the part that
  represents the next-state behavior

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8.4 Hardwired Control

• Sequence Register and Decoder
• provide an output signal corresponding to each of
  the states
• A register with n F/Fs can have up to 2n
  states n-to-2n decoder has up to 2n
  outputs, one for each of the states
• consist of 3 states and 2 inputs
• ? 2 F/Fs and 2-to-4-line decoder

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8.4 Hardwired Control

• state table for the sequencing part
• designate 2 F/Fs as M1 M0
• state 00 (IDLE), 01 (MUL0), 10 (MUL1)
• input equations for F/Fs
• DM0 IDLE G MUL1 Z
• DM1 MUL0

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8.4 Hardwired Control

• One Flip-Flip per state
• another possible method of control
  logic design
• A F/F is assigned to each of the state,
• only one of F/F contains a 1, with others 0

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8.4 Hardwired Control

• Control unit with one flip-flop per state
• N f/fs are required.
• Simplicity ? a little design effort

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8.7 Microprogrammed Control

• Micro-programmed control
• a control unit with its binary values stored as
  words in memory
• Micro-instructions
• one or more microinstructions
• Micro-program
• fixed at the time of the system design stored
  in ROM

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8.7 Microprogrammed Control

• ROM
• Contents of a word in ROM specify the
  microoperations to be performed for both the
  datapath the control unit
• CAR (control address register)
• specifies address of microinstruction
• Sequential circuit Moore type
• CDR (control data register)
• holds the microinstructions currently being
  executed by the datapath and the control unit
• for pipelining
• CDR holds the present microinstruction while the
  next address is being computed the next
  microinstruction is being read from memory
• Next-address generator
• produce the next address, depending on inputs
  (status bits)
• Sequencer
• next-address generator combined with CAR

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8.7 Microprogrammed Control
CAR Moore-type sequential circuit - not allow
conditional output box
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8.7 Microprogrammed Control

• status bits enter the next-address generator
  affect the determination of the next state
• 4 control signals are needed for the
  datapath Initialize, Load, Clear_C, Shift_dec
• 4 control signals can be used as given or can be
  encoded to reduce the number of bits in
  microinstruction
• ?? ??, INIT???? ???? control????

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8.7 Microprogrammed Control

• a microprogram for the binary multiplier in
  register transfer notation
• microinstruction corresponds to each of the state
  in ASM chart

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8.7 Microprogrammed Control

• 3 control signal combinations are used
• (Initialize, Clear_C) in state INIT ? 0101
• (Load) in state ADD ?
  0010
• (Clear_C, Shift_dec) in state MUL1 ? 1100
• IDLE, MUL0 ? no control signal ? 0000
• format of the microinstruction control word
• DATAPATH 4-bit code
• NXTADD0, NXTADD1 define the next addresses
  based on decision
• SEL select whether to make a decision
• if so, to select which one of the three
  decision variables G, Q0, Z

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8.7 Microprogrammed Control
- For sequencing the control unit
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8.7 Microprogrammed Control

• Design a control unit
• length of ROM control words 12 bits
• ROM contains 5 words
• since there are only 5 status
• CAR 3-bit parallel load register

Note) - ROM? ?? - CAR? ?? - NAR? ??
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8.7 Microprogrammed Control

• Register transfer micro-program
• symbolic microprogram

Binary representation
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Design of Control Units

• Hardwired control
• For non-programmable system
• Micro-programmed control
• For programmable system

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