computer organization and design memories and state machines montek singh wed, nov 6-11, 2013...
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Computer Organization and Computer Organization and DesignDesign
Memories and State MachinesMemories and State Machines
Montek SinghMontek Singh
Wed, Nov 6-11, 2013Wed, Nov 6-11, 2013
Lecture 13Lecture 13
TopicsTopics Memory ArraysMemory Arrays Transparent LatchesTransparent Latches Edge-triggered RegistersEdge-triggered Registers Finite State MachinesFinite State Machines
Memory as a Lookup TableMemory as a Lookup Table
A multiplexer to implement a lookup table:A multiplexer to implement a lookup table: Remember that, in theory, we can build any 1-output Remember that, in theory, we can build any 1-output
combinational logic block with multiplexerscombinational logic block with multiplexers For an N-input function we need a 2For an N-input function we need a 2NN input multiplexer input multiplexer
BIG Multiplexers?BIG Multiplexers? How about 10-input function? 20-input?How about 10-input function? 20-input?
MUXLogic
A B
Fn(A,B)
AB Fn(A,B)
00 0 01 1 10 1 11 0
A MuxA Mux’’s Gutss Guts
Hmmm, by sharing the decoder part of the logic MUXs could be adapted to make lookup tables with any number of outputs
I 00
I 01
I 10
I 11
AB
AB
AB
AB
Y
Decoder Selector Multiplexerscan be
partitionedinto two sections.
A DECODER thatidentifies the
desired input,and
a SELECTOR that enables that
inputonto the output.
A decodergeneratesall possible
productterms fora set ofinputs
0
1
2
3
A New Combinational DeviceA New Combinational Device
k
D1D2
DN
DECODER:
k SELECT inputs,
N = 2k DATA OUTPUTs.
Selected Dj HIGH; all others LOW.
NOW, we are well on our way to building a general purpose table-lookup device.
We can build a 2-dimensional ARRAY of decoders and selectors as follows ...
Shared Decoding LogicShared Decoding Logic
We can build a general purpose “table-lookup” device called a Read-Only Memory (ROM), from which we can implement any truth table and, thus, any combinational device
Logic According to ROMsLogic According to ROMs ROMs ignore the structure of combinational ROMs ignore the structure of combinational
functions ...functions ... Size, layout, and design are independent of functionSize, layout, and design are independent of function Any Truth table can be Any Truth table can be ““programmedprogrammed”” by minor by minor
reconfiguration:reconfiguration:Metal layer (masked ROMs)Metal layer (masked ROMs)Fuses (Field-programmable PROMs)Fuses (Field-programmable PROMs)Charge on floating gates (EPROMs)Charge on floating gates (EPROMs) ... etc.... etc.
Model: LOOK UP value of function in truth Model: LOOK UP value of function in truth table...table... Inputs: Inputs: ““ADDRESSADDRESS”” of a T.T. entry of a T.T. entry ROM SIZE = # TT entries...ROM SIZE = # TT entries...
... for an N-input boolean function, size = __________... for an N-input boolean function, size = __________
2N x #outputs
Analog Storage: Using CapacitorsAnalog Storage: Using Capacitors WeWe’’ve chosen to encode information using voltages ve chosen to encode information using voltages
and we know from physics that we can and we know from physics that we can ““storestore”” a a voltage as voltage as ““chargecharge”” on a capacitor on a capacitor
Pros:Pros:compact!compact!
Cons:Cons: it leaks! refreshit leaks! refreshcomplex interfacecomplex interface reading a bit, destroys reading a bit, destroys
itit– (you have to rewrite (you have to rewrite
the value after each the value after each read)read)
itit’’s NOT a digital circuits NOT a digital circuit
bit line
N-channel FET serves
as an access switch
VREF
To write: Drive bit line, turn on access fet, force storage cap to new voltageTo read: precharge bit line, turn on access fet, detect (small) change in bit line voltage
wordline
This storage circuit is the basis for commodity DRAMs
Y
S
B
A A ““DigitalDigital”” Storage Element Storage Element ItIt’’s also easy to build a settable DIGITAL s also easy to build a settable DIGITAL
storage element (called a latch) using a MUX storage element (called a latch) using a MUX and FEEDBACK:and FEEDBACK:
0
1
G
0011
D
----01
QIN
01----
QOUT
0101
Q follows D
Q stable
“state” signalappears as bothinput and output
A
D
G
Q
Here’s a feedback path,so it’s no longer acombinational circuit.
Static D LatchStatic D Latch
G
D Q
D
G
Q stable
Q follows D
Positive latch
Q
“static” means latch will hold data (i.e., value of Q) while G is inactive, however long that may be.
G
D Q
Negative latch
Q
G
D
1
0
Latch TimingLatch Timing Circuits with memory must follow some rulesCircuits with memory must follow some rules
Guarantee that inputs to sequential devices are valid Guarantee that inputs to sequential devices are valid and stable during periods when they may influence and stable during periods when they may influence state changesstate changesThis is assured with additional timing specificationsThis is assured with additional timing specifications
G
D
>tPULSE
tPULSE (minimum pulse width): guarantee G is active for long enough for latch to capture data
>tSETUP
tSETUP (setup time): guarantee that D value has propagated through feedback path before latch becomes opaque
>tHOLD
tHOLD (hold time): guarantee latch is opaque and Q is stable before allowing D to change again
Flakey Control SystemsFlakey Control Systems
Here’s a strategy for saving 2 bucks the next time you find yourself at a toll booth!
Flakey Control SystemsFlakey Control Systems
Here’s a strategy for saving 2 bucks the next time you find yourself at a toll booth!
Flakey Control SystemsFlakey Control Systems
WARNING:Professional Drivers Used!
DON’T try thisAt home!
Here’s a strategy for saving 2 bucks the next time you find yourself at a toll booth!
Escapement StrategyEscapement Strategy
The Solution: Add two gates and only open one at a time.
Escapement StrategyEscapement Strategy
The Solution: Add two gates and only open one at a time.
Escapement StrategyEscapement Strategy
The Solution: Add two gates and only open one at a time.
Escapement StrategyEscapement Strategy
The Solution: Add two gates and only open one at a time. (Psst… Don’t tell the toll folks)
Escapement StrategyEscapement Strategy
The Solution: Add two gates and only open one at a time. (Psst… Don’t tell the toll folks)
Escapement StrategyEscapement Strategy
The Solution: Add two gates and only open one at a time. (Psst… Don’t tell the toll folks)
Escapement StrategyEscapement Strategy
The Solution: Add two gates and only open one at a time. (Psst… Don’t tell the toll folks)
Escapement StrategyEscapement Strategy
The Solution: Add two gates and only open one at a time.
Escapement StrategyEscapement Strategy
The Solution: Add two gates and only open one at a time.
Escapement StrategyEscapement Strategy
The Solution: Add two gates and only open one at a time. (Psst… Don’t tell the toll folks)
Escapement StrategyEscapement Strategy
The Solution: Add two gates and only open one at a time. (Psst… Don’t tell the toll folks)
Escapement StrategyEscapement Strategy
The Solution: Add two gates and only open one at a time. (Psst… Don’t tell the toll folks)
Escapement StrategyEscapement Strategy
The Solution: Add two gates and only open one at a time. (Psst… Don’t tell the toll folks)
Escapement StrategyEscapement Strategy
The Solution: Add two gates and only open one at a time.
Escapement StrategyEscapement Strategy
The Solution: Add two gates and only open one at a time.
Escapement StrategyEscapement Strategy
The Solution: Add two gates and only open one at a time. (Psst… Don’t tell the toll folks)
Key Idea: At no time is there an open path through both gates…
G
D Q
G
D Q
Edge-triggered Flip FlopEdge-triggered Flip Flop
Logical Logical ““escapementescapement””:: Double-gated toll booth built using logic gatesDouble-gated toll booth built using logic gates
Observations:Observations: only one latch only one latch ““transparenttransparent”” at any time: at any time:
master closed when slave is open (CLK is high)master closed when slave is open (CLK is high)slave closed when master is open (CLK is low)slave closed when master is open (CLK is low)no combinational path all the way through flip flopno combinational path all the way through flip flop
Q only changes shortly after 0 Q only changes shortly after 0 1 1 transition transition of CLK, so of CLK, so flip flop appears to be flip flop appears to be ““triggeredtriggered”” by rising edge of by rising edge of CLKCLK
D QD
CLK
Q D
CLK
Qmaster slav
e
Transitions mark instants, not
intervals
Flip Flop WaveformsFlip Flop Waveforms
G
D Q
G
D Q D QD
CLK
Q D
CLK
Qmaster slav
e
D
CLK
Q
master closedslave open
slave closedmaster open
Flip Flop TimingFlip Flop Timing
CLK
D
QD QD
CLK
Q<tPD
tPD: maximum propagation delay, CLK Q >tSETUP
tSETUP: setup timeguarantee that D has propagated through feedback path before master closes
>tHOLD
tHOLD: hold timeguarantee master is closed and data is stable before allowing D to change
Synchronous SystemsSynchronous Systems
Designing digital systems using a clockDesigning digital systems using a clock
Synchronous SystemsSynchronous Systems
FlipflopCombinational
logicFlipflop
leading
edge
trailing
edge
On the leading edge of the clock, the input of a flipflop is transferred to the output and held.
We must be sure the output of the combinational logic has settled before the next leading clock edge.
Clock
data
Clock period must be “long enough”Clock Period >= tFF + tlogic + tsetup
Finite State MachinesFinite State Machines What is a State Machine?What is a State Machine?
Remember automata?Remember automata?
It is defined by the following:It is defined by the following:Set of STATESSet of STATESSet of INPUTSSet of INPUTSSet of OUTPUTSSet of OUTPUTSA mapping from (STATES, INPUTS) to …A mapping from (STATES, INPUTS) to …
… … the next STATE and an OUTPUTthe next STATE and an OUTPUT
STATE represents memory!STATE represents memory!
Implementing an FSMImplementing an FSM Use flipflops to represent state (i.e., memory)Use flipflops to represent state (i.e., memory) Use combinational logic to compute:Use combinational logic to compute:
output as a function of inputs + stateoutput as a function of inputs + state next state as a function of inputs + statenext state as a function of inputs + state
State(flipflops)
Function
(comb. logic)
Inputs Outputs
Clock
Example: Traffic Light ControllerExample: Traffic Light Controller 4 states4 states
each corresponding to a each corresponding to a circlecircle
represent states using 2 represent states using 2 bitsbits00, 01, 10, 1100, 01, 10, 11
4 bits of output4 bits of output 2 bits for east/west light2 bits for east/west light 2 bits for north/south light2 bits for north/south light
Red (00)Red (00)Yellow (01)Yellow (01)Green (10)Green (10)
G E/W
R N/S
Y E/W
R N/S
R E/W
G N/S
R E/W
Y N/S
Example: Traffic Light ControllerExample: Traffic Light Controller 4 states4 states
00, 01, 10, 1100, 01, 10, 11need 2 flipflops to need 2 flipflops to
represent staterepresent state
4 bits of output4 bits of outputR (00), Y (01), G (10)R (00), Y (01), G (10)
Truth table:Truth table: this defines the this defines the
combinational logic part of combinational logic part of the FSMthe FSM
G E/W
R N/S
Y E/W
R N/S
R E/W
G N/S
R E/W
Y N/S
Input (State) Output Next State
00 10 00 01
01 01 00 10
10 00 10 11
11 00 01 00
SummarySummary Regular Arrays can be used to implement Regular Arrays can be used to implement
arbitrary logic functions arbitrary logic functions MemoriesMemories
ROMs are HARDWIRED memoriesROMs are HARDWIRED memories RAMs include storage elements that are read-writeRAMs include storage elements that are read-write
dynamic memory: compact, only reliable short-termdynamic memory: compact, only reliable short-termstatic memory: controlled use of positive feedbackstatic memory: controlled use of positive feedback
For static storage:For static storage: Level-sensitive D-latches; edge-triggered flipflopsLevel-sensitive D-latches; edge-triggered flipflops Timing issues: setup and hold timesTiming issues: setup and hold times
Finite State Machines:Finite State Machines: Implement using flipflops for memory, and Implement using flipflops for memory, and
combinational logic to compute output, next statecombinational logic to compute output, next state
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