ECEN 248: INTRODUCTION TO
DIGITAL SYSTEMS DESIGN
Dr. Shi
Dept. of Electrical and Computer Engineering
Random Access Memory (RAM)
Static (SRAM) and Dynamic
(DRAM)
SRAMs

Static Random Access Memory (SRAM)


Each bit is a latch made of 6 to 8 transistors.
Fast, used for CPU cache
World Line to select
Bit Line to read/write
DRAMs

Dynamic Random Access Memory



Each bit (cell) uses 1 capacitor and 1 transistor
Charge will leak, so need to refresh every few us
Inexpensive, used for main memory
Flash Memory: Non-volatile RAM


Both SRAM and DRAM will lose its content when
power is turned off
Flash memory hold data in “floating gate”
READ ONLY MEMORIES (ROM)
Overview



Read-only memory can normally only be read
Internal organization similar to SRAM
ROMs are effective at implementing truth tables
 Any


logic function can be implemented using ROMs
Multiple single-bit functions embedded in a single
ROM
Also used in computer systems for initialization
 ROM

doesn’t lose storage value when power is removed
Very useful for implementing FSMs
Read-Only Memory (ROM)

An array of semiconductor devices
 diodes
 transistors
 field


effect transistors
2N words by M bits
Data can be read but not changed
 (normal
operating conditions)
Read-Only Memory (ROM)

N input bits

2N words by M bits

Implement M arbitrary functions of N variables

Example 8 words by 5 bits:
3 Input
Lines
A
B
C
ROM
8 words
x 5 bits
F0
F1 F2
F3
F4
5 Output Lines
ROM Implementation

ROM = "Read Only Memory"


A ROM can be used to implement a truth table



values of memory locations are fixed ahead of time
if the address is m-bits, we can address 2m entries in the ROM.
our outputs are the bits of data that the address points to.
ROM is a combinational device, not a sequential one
m

n
m is the "height", and n is the "width"
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
ROM Implementation

Suppose there are 10 inputs
10 address lines (i.e., 210 = 1024 different
addresses)
Suppose there are 20 outputs

ROM is 210 x 20 = 20K bits

Rather wasteful, since lots of storage bits


For functions, doesn’t take advantage of K-maps,
other minimizations
Read-Only Memory (ROM)
Each minterm of each function can be specified
3 Inputs
Lines
A
B
C
ROM
8 words
x 5 bits
F0
F1 F2
F3
F4
5 Outputs Lines
A
B
C
F0
F1
F2 F3 F4
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
1
0
ROM Internal Structure
n Inputs
Lines
..
.
n bit
decoder
.
.
.
Memory Array
2n words x m bits
...
m Outputs Lines
ROM Memory Array
m0=A’B’C’
m1=A’B’C
m2=A’BC’
A
B
C
3 to 8
decoder
m3=A’BC
m4=AB’C’
m5=AB’C
m6=ABC’
m7=ABC
F0
F1
F2
F3
F4
Inside the ROM

Alternate view
 Each
possible horizontal/vertical intersection indicates a
possible connection

Or gates at bottom output the word selected by the
decoder (32 x 8)
ROM Example
Specify a truth table for a ROM which implements:
F = AB + A’BC’
G = A’B’C + C’
H = AB’C’ + ABC’ + A’B’C
A
B
C
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
F
G
H
ROM Example
Specify a truth table for a ROM which implements:
F = AB
+ A’BC’
G = A’B’C + C’
H = AB’C’ + ABC’ + A’B’C
A
B
C
F
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
G
H
ROM Example
Specify a truth table for a ROM which implements:
F = AB + A’BC’
G = A’B’C + C’
H = AB’C’
+
ABC’ + A’B’C
A
B
C
F
G
H
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
Function Implementation
m0=A’B’C’
m1=A’B’C
m2=A’BC’
A
B
C
3 to 8
decoder
m3=A’BC
m4=AB’C’
m5=AB’C
m6=ABC’
m7=ABC
Each column is a new function
Note: two outputs unused!
F
G
H
ROM Implementation of a Moore Machine



ROMs implement combinational logic
Note that ROMs do not hold state
How would you determine the maximum clock
frequency of this circuit?
 Look
Input
s
at the FF to FF path (NS to PS)
ROM
Present
State
Next
State
ROM
Outputs
ROM Implementation of a Mealy Machine



ROMs implement combinational logic
Note that ROMs do not hold state
How would you determine the maximum clock
frequency of this circuit?
 Look
Inputs
at the FF to FF path (NS to PS)
ROM
Present
State
Next
State
ROM
Outputs
Summary


ROMs provide stable storage for data
ROMs have address inputs and data outputs
 ROMs


ROMs can be used effectively in Mealy and Moore
machines to implement combinational logic
In normal use ROMs are read-only
 They

directly implement truth tables
are only read, not written
ROMs are often used by computers to store critical
information
 Unlike
SRAM, they maintain their storage after the power
is turned off
PROGRAMMABLE LOGIC ARRAYS
(PLA)
Programmable logic arrays
24


A ROM is potentially inefficient because it uses a
decoder, which generates all possible minterms. No
circuit minimization is done.
Using a ROM to implement an n-input function
requires:
n-to-2n decoder, with n inverters and 2n n-input AND
gates.
n
 An OR gate with up to 2 inputs.
 The number of gates roughly doubles for each
additional ROM input.
 An
Programmable logic arrays
25

A programmable logic array, or PLA, makes the
decoder part of the ROM “programmable” too.
Instead of generating all minterms, you can choose
which products (not necessarily minterms) to
generate.
A blank 3 x 4 x 3Inputs
PLA
26

This is a 3 x 4 x 3
PLA (3 inputs, up
to 4 product
terms, and 3
outputs), ready to
be programmed.
OR array
AND array
Outputs
PLA example
27
x
y
z
xy’z’
xy
x’z
x’yz’
V2 = m(1,2,3,4)= xy’z’ + x’z + x’yz’
V1 = m(2,6,7) = x’yz’ + xy
V0 = m(4,6,7) = xy’z’ + xy
V2
V1
V0
PLA evaluation
28


A k x m x n PLA can implement up to n functions of
k inputs, each of which must be expressible with no
more than m product terms.
Unlike ROMs, PLAs allow you to choose which
products are generated.
 This
can significantly reduce the fan-in (number of
inputs) of gates, as well as the total number of gates.
 However, a PLA is less general than a ROM. Not all
functions may be expressible with the limited number of
AND gates in a given PLA.