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CS2100 Computer Organisation
Sequential Logic
2011 Sem 1 Sequential Logic 2
SEQUENTIAL LOGIC
➤ Memory Elements➤ Latches: S-R Latch, D Latch➤ Flip-flops: S-R flip-flop, D flip-flop, J-K flip-flops, T flip-flops➤ Asynchronous Inputs➤ Finite State Machines➤ Memory➤ Memory Unit➤ Read/Write Operations➤ Memory Arrays
2011 Sem 1 Sequential Logic 3
INTRODUCTION (1/2)
➤ Two classes of logic circuits– Combinational– Sequential
➤ Combinational Circuit– Each output depends entirely
on the immediate (present) inputs.
CombinationalLogic: :inputs outputs: :
➤ Sequential Circuit– Each output depends on both
present inputs and state.
Memory
CombinationalLogic: :inputs outputs: :
2011 Sem 1 Sequential Logic 4
INTRODUCTION (2/2)
➤ Two types of sequential circuits:– Synchronous: outputs change only at specific time– Asynchronous: outputs change at any time
➤ Multivibrator: a class of sequential circuits– Bistable (2 stable states)– Monostable or one-shot (1 stable state)– Astable (no stable state)
➤ Bistable logic devices– Latches and flip-flops.– They differ in the methods used for changing their state.
2011 Sem 1 Sequential Logic 5
MEMORY ELEMENTS (1/3)
➤ Memory element: a device which can remember value indefinitely, or change value on command from its inputs.
command Memory element stored value
Q
➤ Characteristic table:
Command(at time t)
Q(t) Q(t+1)
Set X 1
Reset X 0
0 0Memorise /No Change 1 1
Q(t) or Q: current state
Q(t+1) or Q+: next state
2011 Sem 1 Sequential Logic 6
MEMORY ELEMENTS (2/3)
➤ Memory element with clock.
➤ Clock is usually a square wave.
command Memory element stored value
Q
clock
Positive edges Negative edges
Positive pulses Clock period
If clock period is x seconds, then the clock frequency (or rate) is 1/x Hz. For example, a 2 GHz PC has a clock period of 0.5 nanosecond.
2011 Sem 1 Sequential Logic 7
MEMORY ELEMENTS (2/3)
➤ Memory element with clock.
➤ Clock is usually a square wave.
command Memory element stored value
Q
clock
Positive edges Negative edges
Positive pulses Clock period
The speed of light in vacuum is about 3 x 108 metres per second. In half a nanosecond, light travels 15 cm.
2011 Sem 1 Sequential Logic 8
MEMORY ELEMENTS (3/3)
➤ Two types of triggering/activation– Pulse-triggered– Edge-triggered
➤ Pulse-triggered– Latches– ON = 1, OFF = 0
➤ Edge-triggered– Flip-flops– Positive edge-triggered (ON = from 0 to 1; OFF = other time)– Negative edge-triggered (ON = from 1 to 0; OFF = other time)
Positive edges Negative edges
Positive pulses
2011 Sem 1 Sequential Logic 9
FINITE STATE MACHINES
➤ Built with combinational logic and memory (stores the state)
➤ Next state depends on current state and inputs➤ Many computations can be specified as FSMs➤ Example: counter
ELEMENTS OF A FSM
➤ A finite set of states– One of the state is a special “START” state– Zero or more of the states are “FINAL” state– States are related to one another by state
transitions
➤ A finite set of inputs➤ A finite set of outputs
2011 Sem 1 Sequential Logic 10
EXAMPLE
2011 Sem 1 Sequential Logic 11
B E W P
D
Born Education Work Play
R
Retire
Death
Heart attack
Bored
BoredA
ge =
= 65
Age == 6 GraduateLeave == 0
Vacation over
Start State
Final State
State
State Transition
Input
12
A: X = current_mouse_position();
B: X = current_mouse_position();Draw line from X to Y;
C: Act on line input;
FSM control for rubber banding
Press / A
Move / B
Release / C
2011 Sem 1 Sequential Logic 13
USE CASE EXAMPLE
➤ Two output signals:– NSlite: When this signal is asserted, the light on the north-south road is
green; when this signal is deasserted the light on the north-south road is red.
– EWlite: When this signal is asserted, the light on the east-west road is green; when this signal is deasserted the light on the east-west road is red.
➤ Two inputs: NScar and EWcar.– NScar: Indicates that a car is over the detector placed in the roadbed in
front of the light on the north-south road (going north or south).– EWcar: Indicates that a car is over the detector placed in the roadbed in
front of the light on the east-west road (going east or west).➤ The traffic light should change from one direction to the other only if
a car is waiting to go in the other direction; otherwise, the light should continue to show green in the same direction as the last car that crossed the intersection.
2011 Sem 1 Sequential Logic 14
STATE DIAGRAM
Two states:
• NSgreen: The traffic light is green in the north-south direction
• EWgreen: The traffic light is green in the east-west direction
Memory elements
2011 Sem 1 Sequential Logic 15
2011 Sem 1 Sequential Logic 16
S-R LATCH (1/3)
➤ Two inputs: S and R.➤ Two complementary outputs: Q and Q'.
– When Q = HIGH, we say latch is in SET state.– When Q = LOW, we say latch is in RESET state.
➤ For active-high input S-R latch (also known as NOR gate latch)– R = HIGH and S = LOW Q becomes LOW (RESET state)– S = HIGH and R = LOW Q becomes HIGH (SET state)– Both R and S are LOW No change in output Q – Both R and S are HIGH Outputs Q and Q' are both LOW
(invalid!)
➤ Drawback: invalid condition exists and must be avoided.
2011 Sem 1 Sequential Logic 17
S-R LATCH (2/3)
➤ Active-high input S-R latch:
R
S
Q
Q'
S R Q Q'1 0 1 0 initial0 0 1 0 (afer S=1, R=0)0 1 0 10 0 0 1 (after S=0, R=1)1 1 0 0 invalid!
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
S
R
Q
Q'
➤ Block diagram:
2011 Sem 1 Sequential Logic 18
S-R LATCH (3/3)
➤ Characteristic table for active-high input S-R latch:
S R Q Q'
0 0 NC NC No change. Latchremained in present state.
1 0 1 0 Latch SET.
0 1 0 1 Latch RESET.
1 1 0 0 Invalid condition.
S
R
Q
Q'
S R Q(t+1)
0 0 Q(t) No change
0 1 0 Reset
1 0 1 Set
1 1 indeterminate
Q(t+1) = S + R'Q
SR = 0
2011 Sem 1 Sequential Logic 19
GATED S-R LATCH
➤ S-R latch + enable input (EN) and 2 NAND gates a gated S-R latch.
S
R
Q
Q'
EN
S
EN
R
Q
Q'
➤ Outputs change (if necessary) only when EN is high.
2011 Sem 1 Sequential Logic 20
GATED D LATCH (1/2)
➤ Make input R equal to S' gated D latch.
➤ D latch eliminates the undesirable condition of invalid state in the S-R latch.
D
EN
Q
Q'
DQ
Q'
EN
2011 Sem 1 Sequential Logic 21
GATED D LATCH (2/2)
➤ When EN is high,– D = HIGH latch is SET– D = LOW latch is RESET
➤ Hence when EN is high, Q “follows” the D (data) input.
➤ Characteristic table:
When EN=1, Q(t+1) = D
2011 Sem 1 Sequential Logic 22
FLIP-FLOPS (1/2)
➤ Flip-flops are synchronous (clocked) bistable (two state) devices.
➤ Output changes state at a specified point on a triggering input called the clock.
➤ Change state either at the positive (rising) edge, or at the negative (falling) edge of the clock signal.
Positive edges Negative edges
Clock signal
2011 Sem 1 Sequential Logic 23
FLIP-FLOPS (2/2)
➤ S-R flip-flop, D flip-flop, and J-K flip-flop.
➤ Note the “>” symbol at the clock input.
S
C
R
Q
Q'
D
C
Q
Q'
J
C
K
Q
Q'
Positive edge-triggered flip-flops
S
C
R
Q
Q'
D
C
Q
Q'
J
C
K
Q
Q'
Negative edge-triggered flip-flops
2011 Sem 1 Sequential Logic 24
S-R FLIP-FLOP
➤ S-R flip-flop: On the triggering edge of the clock pulse,– R = HIGH and S = LOW Q becomes LOW (RESET state)– S = HIGH and R = LOW Q becomes HIGH (SET state)– Both R and S are LOW No change in output Q – Both R and S are HIGH Invalid!
➤ Characteristic table of positive edge-triggered S-R flip-flop:
X = irrelevant (“don’t care”)
= clock transition LOW to HIGH
S R CLK Q(t+1) Comments
0 0 X Q(t) No change
0 1 0 Reset
1 0 1 Set
1 1 ? Invalid
S
C
R
Q
Q'
2011 Sem 1 Sequential Logic 25
S-R FLIP-FLOP
CLK
SET
RESET
Q
2011 Sem 1 Sequential Logic 26
D FLIP-FLOP
➤ D flip-flop: Single input D (data). On the triggering edge of the clock pulse,– D = HIGH Q becomes HIGH (SET state)– D = LOW Q becomes LOW (RESET state)
➤ Hence, Q “follows” D at the clock edge.
➤ Convert S-R flip-flop into a D flip-flop: add an inverter.
A positive edge-triggered D flip-flop formed with an S-R flip-flop.
S
C
R
Q
Q'
CLK
DD CLK Q(t+1) Comments
1 1 Set
0 0 Reset
= clock transition LOW to HIGH
2011 Sem 1 Sequential Logic 27
D FLIP-FLOP
CLK
D
Q
2011 Sem 1 Sequential Logic 28
D FLIP-FLOP vs D LATCH
D
CLK for FFConnect to EN for latch
Q forD-latch
Q forD-flip-flop
Enabled!
2011 Sem 1 Sequential Logic 29
D FLIP-FLOP
➤ Application: Parallel data transfer.– To transfer logic-circuit outputs X, Y, Z to flip-flops Q1, Q2 and
Q3 for storage.
* After occurrence of negative-going transition
Q1 = X*D
CLK
Q
Q'
Q2 = Y*D
CLK
Q
Q'
Q3 = Z*D
CLK
Q
Q'
Combinational logic circuit
Transfer
X
Y
Z
2011 Sem 1 Sequential Logic 30
J-K FLIP-FLOP (1/2)
➤ J-K flip-flop: Q and Q' are fed back to the pulse-steering NAND gates.
➤ No invalid state.
➤ Include a toggle state– J = HIGH and K = LOW Q becomes HIGH (SET state)– K = HIGH and J = LOW Q becomes LOW (RESET state)– Both J and K are LOW No change in output Q – Both J and K are HIGH Toggle
2011 Sem 1 Sequential Logic 31
J-K FLIP-FLOP (2/2)
➤ J-K flip-flop circuit:
JQ
Q'
CLK
Pulse transition detector
K
➤ Characteristic table:
J K CLK Q(t+1) Comments
0 0 Q(t) No change
0 1 0 Reset
1 0 1 Set
1 1 Q(t)' Toggle
Q J K Q(t+1)
0 0 0 0
0 0 1 0
0 1 0 1
0 1 1 1
1 0 0 1
1 0 1 0
1 1 0 1
1 1 1 0Q(t+1) = JQ' + K'Q
2011 Sem 1 Sequential Logic 32
Pulse detection circuit
Positive edge detection
Propagation delay of the NOT gate
2011 Sem 1 Sequential Logic 33
Pulse detection circuit
Positive edge detection Negative edge detection
Propagation delay of one NOT gate
2011 Sem 1 Sequential Logic 34
T FLIP-FLOP
➤ T flip-flop: Single input version of the J-K flip-flop, formed by tying both inputs together.
➤ Characteristic table:
TQ
Q'
CLK
Pulse transition detector
J
C
K
Q
Q'
CLK
T
T CLK Q(t+1) Comments
0 Q(t) No change
1 Q(t)' Toggle
Q T Q(t+1)
0 0 0
0 1 1
1 0 1
1 1 0Q(t+1) = TQ' + T'Q
2011 Sem 1 Sequential Logic 35
Frequency Divider
QCLK
CLK
Q
Frequency = f
Frequency = f / 2
2011 Sem 1 Sequential Logic 36
Frequency Divider
➤ What does this do?
2011 Sem 1 Sequential Logic 37
A 4 bit counterA B C D
CLK
• CLK is at frequency f: 1010101010101010101010101010101010
• D is at frequency f/2: 110011001100110011001100110011001111
• C is at frequency f/4: 111100001111000011110000111100001111
• B is at frequency f/8: 1111111100000000111111110000000011111111
• A is at frequency f/16: 11111111111111110000000000000000
• Recall our truth table! Count down…
2011 Sem 1 Sequential Logic 38
Counter from scratchABCD0000000100100011010001010110011110001001101010111100110111101111
• Bit D changes every clock cycle
• Easy – just use a JK flip flop
D
2011 Sem 1 Sequential Logic 39
Counter from scratchABCD0000000100100011010001010110011110001001101010111100110111101111
• Bit C toggles when D is 1 in the previous cycle
• It does not change when D is 0 in the previous cycle
D C
2011 Sem 1 Sequential Logic 40
Counter from scratchABCD0000000100100011010001010110011110001001101010111100110111101111
• Bit B toggles when C and D are both 1 in the previous cycle
• It does not change otherwise
D C B
2011 Sem 1 Sequential Logic 41
Counter from scratchABCD0000000100100011010001010110011110001001101010111100110111101111
• Bit A toggles when B and C and D are all 1 in the previous cycle
• It does not change otherwise
D C BA
2011 Sem 1 Sequential Logic 42
Decimal counterABCD0000000100100011010001010110011110001001000000010010001101000111
• Bit A toggles when B and C and D are all 1 in the previous cycle
• Both bit A and C to be set to 0 when A and D are both 1 in the previous cycle
• When A is 1, disallow any toggling of C (use D’)
ABCD
2011 Sem 1 Sequential Logic 43
Frequency Divider (Odd)
CLK
A
B
CLK
Frequency = f
A
B
Frequency = f / 3
Design methodology for sequential logic
The Moore Machine
➤ Output depends only on the current state
➤ Synchronous counters
2011 Sem 1 Sequential Logic 45
Example: 3-bit binary counter
Present State Next State
A B C A B C
0 0 0 0 0 1
0 0 1 0 1 0
0 1 0 0 1 1
0 1 1 1 0 0
1 0 0 1 0 1
1 0 1 1 1 0
1 1 0 1 1 1
1 1 1 0 0 0
2011 Sem 1 Sequential Logic 46
Step 1: Formulate the problem either as a truth table or a finite state machine
Step 2: Assign flip-flops
➤ Will use one flip-flop for each of the current state bits– 3 JK flip-flops for A, B, and C, respectively
2011 Sem 1 Sequential Logic 47
Step 3: Draw truth table for flip-flop inputs
Present State Next State
A B C A B C JA KA JB KB JC KC
0 0 0 0 0 1 0 X 0 X 1 X
0 0 1 0 1 0 0 X 1 X X 1
0 1 0 0 1 1 0 X X 0 1 X
0 1 1 1 0 0 1 X X 1 X 1
1 0 0 1 0 1 X 0 0 X 1 X
1 0 1 1 1 0 X 0 1 X X 1
1 1 0 1 1 1 X 0 X 1 1 X
1 1 1 0 0 0 X 1 X 0 X 1
2011 Sem 1 Sequential Logic 48
Q J K Q(t+1)
0 0 0 0
0 0 1 0
0 1 0 1
0 1 1 1
1 0 0 1
1 0 1 0
1 1 0 1
1 1 1 0
Step 3: K-map
00 01 11 10
0 0 0 1 0
1 X X X X
2011 Sem 1 Sequential Logic 49
ABC
JA = BC
00 01 11 10
0 X X X X
1 0 0 1 0
ABC
KA = BC
00 01 11 10
0 0 1 X X
1 0 1 X X
ABC
JB = C
00 01 11 10
0 X X 1 0
1 X X 1 0
ABC
KB = C
Step 3: K-map cont’d
00 01 11 10
0 1 X X 1
1 1 X X 1
2011 Sem 1 Sequential Logic 50
ABC
JC = 1
00 01 11 10
0 X 1 1 X
1 X 1 1 X
ABC
KC = 1
Step 4: Circuit Implementation
2011 Sem 1 Sequential Logic 51
USING T-FLIP-FLOPS INSTEAD
Present State Next State
A B C A B C TA TB TC
0 0 0 0 0 1 0 0 1
0 0 1 0 1 0 0 1 1
0 1 0 0 1 1 0 0 1
0 1 1 1 0 0 1 1 1
1 0 0 1 0 1 0 0 1
1 0 1 1 1 0 0 1 1
1 1 0 1 1 1 0 1 1
1 1 1 0 0 0 1 1 1
2011 Sem 1 Sequential Logic 52
Q T Q(t+1)
0 0 0
0 1 1
1 0 1
1 1 0
K-MAPS FOR T-FLIP-FLOPS
2011 Sem 1 Sequential Logic 53
00 01 11 10
0 0 0 1 0
1 0 0 1 0
ABC
TA = BC
00 01 11 10
0 0 1 1 0
1 0 1 1 0
ABC
TB = C
00 01 11 10
0 1 1 1 1
1 1 1 1 1
ABC
TC = 1
Sychronous 3-bit counter using T-flip-flops
2011 Sem 1 Sequential Logic 54
T
CLK
QT
CLK
QT
CLK
Q
A B C
CLK
1
THE MEALY MACHINE
➤ Output is both a function of an input and the current state
➤ Most finite state machines
2011 Sem 1 Sequential Logic 55
EXAMPLE OF A MEALY FSM
2011 Sem 1 Sequential Logic 56
0
1
3
2
0
0
1
0 0
1
1
1
Use 2 JK flip-flops for the 4 states
Truth table for flip-flop inputs
Present State
Input Next State
A B X A B JA KA JB KB
0 0 0 0 1 0 0 1 0
0 0 1 0 0 0 0 0 1
0 1 0 1 1 1 1 1 0
0 1 1 1 0 1 0 0 1
1 0 0 1 1 0 0 1 1
1 0 1 1 0 0 0 0 0
1 1 0 0 0 1 1 1 1
1 1 1 1 1 1 0 0 0
2011 Sem 1 Sequential Logic 57
Q J K Q(t+1)
0 0 0 0
0 0 1 0
0 1 0 1
0 1 1 1
1 0 0 1
1 0 1 0
1 1 0 1
1 1 1 0
Step 3: K-map
00 01 11 10
0 0 0 1 1
1 0 0 1 1
2011 Sem 1 Sequential Logic 58
ABX
JA = B
00 01 11 10
0 0 0 0 1
1 0 0 0 1
ABX
KA = BX
00 01 11 10
0 1 0 0 1
1 1 0 0 1
ABX
JB = X’
00 01 11 10
0 0 1 1 0
1 1 0 0 1
ABX
KB = AX’ + A’X = A ⊕ X
IMPLEMENTATION OF FSM
2011 Sem 1 Sequential Logic 59
J
K
CLK
Q A
J
K
CLK
Q B
CLK
X
2011 Sem 1 Sequential Logic 60
ASYNCHRONOUS INPUTS (1/2)
➤ S-R, D and J-K inputs are synchronous inputs, as data on these inputs are transferred to the flip-flop’s output only on the triggered edge of the clock pulse.
➤ Asynchronous inputs affect the state of the flip-flop independent of the clock; example: preset (PRE) and clear (CLR) [or direct set (SD) and direct reset (RD)].
➤ When PRE=HIGH, Q is immediately set to HIGH.
➤ When CLR=HIGH, Q is immediately cleared to LOW.
➤ Flip-flop in normal operation mode when both PRE and CLR are LOW.
2011 Sem 1 Sequential Logic 61
ASYNCHRONOUS INPUTS (2/2)➤ A J-K flip-flop with active-low PRESET and CLEAR
asynchronous inputs.
JQ
Q'
CLK
Pulse transition detector
K
PRE
CLR
J
C
K
Q
Q'
PRE
CLR
PRE
CLR
CLK
QPreset Toggle ClearJ = K = HIGH
2011 Sem 1 Sequential Logic 62
METASTABILITY (1/3)
CLOCK
DATA
OUTPUT
ts th
tco
ts – setup timeth – hold timetco – clock to output time (propagation delay)
In reality, nothing is instantaneous. Critical timing parameters must be observed.
2011 Sem 1 Sequential Logic 63
METASTABILITY (2/3)
➤ If setup and hold times are violated, flip-flop may oscillate in an indeterminate state between 0 and 1
➤ This is called metastability➤ Introduces error in the circuit’s operation➤ Cannot be absolutely avoided in practice
– Make sure clock period is long enough– Use flip-flop chain
2011 Sem 1 Sequential Logic 64
METASTABILITY (3/3)
➤ The probability of metastability gets closer and closer to zero (but never zero) as the number of flip-flops
connected in series is increased.
D Q D Q
CLK
Input Output
2011 Sem 1 Sequential Logic 65
TRI-STATE MULTIPLEXERS
➤ “Tri-state” = high, low, high-impedance– High-impedance means the circuit
is “not connected”
➤ A tri-state buffer:– When enabled, connects input to
output– When disabled disconnects input
from output by entering a high-impedance state
2011 Sem 1 Sequential Logic 66
MEMORY HIERARCHY (1/2)
➤ Memory stores programs and data.
➤ Definitions:– 1 byte = 8 bits– 1 word: in multiple of bytes, a unit of transfer between main
memory and registers, usually size of register.
– 1 KB (kilo-bytes) = 210 bytes; 1 MB (mega-bytes) = 220 bytes;1 GB (giga-bytes) = 230 bytes; 1 TB (tera-bytes) = 240 bytes.
➤ Desirable properties: fast access, large capacity, economincal cost, non-volatile.
➤ However, most memory devices do not possess all these properties.
2011 Sem 1 Sequential Logic 67
MEMORY HIERARCHY (2/2)
registers
main memory
disk storage
magnetic tapes
Fast, expensive (small numbers), volatile
Slow, cheap (large numbers), non-volatile
➤ Memory hierarchy
2011 Sem 1 Sequential Logic 68
REGISTER FILE (1/2)
➤ A register is an array of D-flip-flops➤ A register file is a circuit with several registers, and
selection lines to choose on which register to operate next
➤ Operations: read and writeFeatures: - Fast - Simple addressing - Multiported (multiple reads and writes concurrently)
2011 Sem 1 Sequential Logic 69
REGISTER FILE (2/2)
D Q
CLK
D Q
CLK
D Q
CLK
D Q
CLK
WR
DecoderRegisterNumber
Read data
Write data
4-bit register
2011 Sem 1 Sequential Logic 70
MEMORY (1/2)
➤ Data transferAddress
k-bit address bus
012345
Processor
MAR
MDR
Memory
:
n-bit data bus
Control lines(R/W, etc.)
Up to 2k addressable
locations.
2011 Sem 1 Sequential Logic 71
MEMORY (2/2)
A memory unit stores binary information in groups of bits called words.
The data consists of n lines (for n-bit words). Data input lines provide the information to be stored (written) into the memory, while data output lines carry the information out (read) from the memory.
The address consists of k lines which specify which word (among the 2k words available) to be selected for reading or writing.
The control lines Read and Write (usually combined into a single control line Read/Write) specifies the direction of transfer of the data.
2011 Sem 1 Sequential Logic 72
MEMORY UNIT
➤ Block diagram of a memory unit:
Memory unit2k words
n bits per word
k address linesk
Read/Write
n
n
n data input lines
n data output lines
2011 Sem 1 Sequential Logic 73
READ/WRITE OPERATIONS
➤ Write operation:– Transfers the address of the desired word to the address lines.– Transfers the data bits (the word) to be stored in memory to the
data input lines.– Activates the Write control line (set Read/Write to 0).
➤ Read operation:– Transfers the address of the desired word to the address lines.– Activates the Read control line (set Read/Write to 1).
Memory Enable Read/Write Memory Operation
0 X None1 0 Write to selected word1 1 Read from selected word
2011 Sem 1 Sequential Logic 74
MEMORY CELL➤ Two types of RAM
– Static RAMs use flip-flops as the memory cells.– Dynamic RAMs use capacitor charges to represent data. Though simpler in
circuitry, they have to be constantly refreshed.
➤ A single memory cell of the static RAM has the following logic and block diagrams:
R
S QInput
Select
Output
Read/Write
BC OutputInput
Select
Read/Write
Logic diagram Block diagram
2011 Sem 1 Sequential Logic 75
MEMORY ARRAYS (1/4)
➤ Logic construction of a 43 RAM (with decoder and OR gates):
2011 Sem 1 Sequential Logic 76
MEMORY ARRAYS (2/4)
➤ An array of RAM chips: memory chips are combined to form larger memory.
➤ A 1K 8-bit RAM chip:
Block diagram of a 1K x 8 RAM chip
RAM 1K x 8
DATA (8)ADRS (10)CSRW
Input dataAddress
Chip selectRead/write
(8) Output data8 810
2011 Sem 1 Sequential Logic 77
MEMORY ARRAYS (3/4)
➤ 4K 8 RAM.
1K x 8
DATA (8)ADRS (10)CSRW
Read/write
(8)
Output data
1K x 8
DATA (8)ADRS (10)CSRW
(8)
1K x 8
DATA (8)ADRS (10)CSRW
(8)
1K x 8
DATA (8)ADRS (10)CSRW
(8)
0–1023
1024 – 2047
2048 – 3071
3072 – 4095
Input data8 lines
0123
2x4 decoder
Lines Lines0 – 911 10
S0
S1
Address
2011 Sem 1 Sequential Logic 78
MEMORY ARRAYS (4/4)
➤ 2M 32 memory module– Using 512K 8 memory chips.Chip select
512K x 8 memory chip
19-bitaddress
8-bit datainput/output
19-bit internal chip address
2-bitdecoder
addresses21-bit
A 0A 1
A19
512k X 8memory chip
A20
D31-24 D7-0D23-16 D 15-8
2011 Sem 1 Sequential Logic 79
END