- A memory device is a gadget
that helps you
record information
and recall
the information at some later time.
Example:
- Requirement of a memory device:
- A memory device
must have more than 1 states
(Otherwise, we can't tell the difference)
Example:
Memory device in state 0 Memory device in state 1 
- A memory device
must have more than 1 states
- The electrical switch
is a memory device:
- The electrical switch can be
in one of these 2 states:
- off (we will call this state 0)
- on (we will call this state 1)
- One switch can
be in one of 2 states
- A row of n switches:
can be in one of 2n states !
- Example: row of 3 switches
A row of 3 switches can be in one of 23 = 8 states.
The 8 possible states are given in the figure above.
- We saw how information can be
represented by number
by using a code (agreement)
Recall: we can use numbers to represent marital status information:
- 0 = single
- 1 = married
- 2 = divorced
- 3 = widowed
- 0 = single
- We can represent each number
using a different state of
the switches.
Example:
- To complete the knowledge on
how information
is represented inside the computer,
we will now study:
- How to use the different states of the switches to represent different numbers
The representation scheme has a chic name:
- the binary number system
Note to lecturer:
- Don't explain all the details on binary number system - this will be explained in CS255
- In CS170, students only need to know that numbers can be encoded by 1's and 0's.
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- The binary number system uses
2 digits to encode
a number:
- 0 = represents no value
- 1 = represents a unit value
That means that you can only use the digits 0 and 1 to write a binary number
Example: some binary numbers
- 0
- 1
- 10
- 11
- 1010
- and so on.
- The value that is
encoded (represented) by a
binary number is computed
as follows:
Binary number Value encoded by the binary number dn-1 dn-2 ... d1 d0 dn-1×2n-1 + dn-2×2n-2 + ... + d1×21 + d0×20 Example:
Binary number Value encoded by the binary number 0 0×20 = 0 1 1×20 = 1 10 1×21 + 0 ×20 = 2 11 1×21 + 1 ×20 = 3 1010 1×23 + 0×22 + 1×21 + 0×20 = 8 + 2 = 10
- Now you should understand how the
different states of
these 3 switches represent the numbers
0-7 using the
binary number system:
- Try to understand this joke:
(Read: there are binary 10 (= 2) types of people: those who understand binary (numbers) and those who don't)
- A knock off joke:
- Recall what we have learned about the
Computer RAM memory:
- The RAM consists of
multiple memory cells:
Each memory cell stores a number
- The RAM consists of
multiple memory cells:
- The connection between
the computer memory and
the binary number system is:
- The computer system uses
the binary number encoding to
store the number
Example:
- Note: the address
is also
expressed as a binary number
A computer can have over 4,000,000,000 bytes (4 Gigabytes) of memory.
So we need a 32 bites to express the address
- The computer system uses
the binary number encoding to
store the number
- A computer is an
electronic device
- Structure of a RAM memory:
- The RAM memory used by
a computer consists of a
large number of electronic switches
- The switches are organized in
rows
For historical reason, the number of switches in one row is 8
Details:
- In order to store text information
in a computer, we need to encode:
- 26 upper case letters ('A', 'B', and so on)
- 26 lower case letters ('a', 'b', and so on)
- 10 digits ('0', '1', and so on)
- 20 or so special characters ('&', '%', '$', and so on)
for a total of about 100 different symbols
- The nearest
power 2n that is larger than
100 is:
- 27 = 128 ≥ 100
- For a reason beyond the scope of this course, an 8th switches is added
- In order to store text information
in a computer, we need to encode:
- This is what a
portion of
the RAM memory looks like:
- What information is stored
in the RAM memory depends on:
- The type of data
(this is the context information)
Example of types: marital status, gender, age, salary, and so on.
- This determines the encoding scheme used to interpret the number
- The type of data
(this is the context information)
- The RAM memory used by
a computer consists of a
large number of electronic switches
- Computer memory jargon:
- bit =
(binary
digit)
a smallest memory device
A bit is in fact a switch that can remember 0 or 1
(The digits 0 and 1 are digits used in the binary number system)
- Byte =
8 bits
A byte is in fact one row of the RAM memory
- KByte = kilo byte =
1024 (= 210) bytes
(approximately 1,000 bytes)
MByte = mega byte = 1048576 (= 220) bytes (approximately 1,000,000 bytes)
GByte = giga byte = 1073741824 (= 230) bytes (approximately 1,000,000,000 bytes)
TByte = tera byte
- bit =
(binary
digit)
a smallest memory device
- A byte
has 8 bits
and therefore, it can store:
- 28 = 256
different patterns
(These 256 patterns are: 00000000, 00000001, 00000010, 00000011, .... 11111111)
- 28 = 256
different patterns
- Each pattern can
are encoded
exactly one number:
- 00000000 = 0
- 00000001 = 1
- 00000010 = 2
- 00000011 = 3
- ...
- 11111111 = 255
Therefore, one byte can store one of 256 possible values
(You can store the number 34 into a byte, but you cannot store the number 556, the value is out of range)
- Exploratory stuff:
- The following computer program illustrates
the effect of the
out of range phenomenon:
public class test { public static void main(String args[]) { byte x = (byte) 556; System.out.println(x); } }
- Compile and run:
>> javac test.java >> java test 44
- This phenomenon is called
overflow
(memory does not have enough space to represent the value)
This is the same phenomenon when you try to compute 1/0 with a calculator; except that the calculator was programmed (by the manufacturer) to reported the error (and the computer is not).
- The following computer program illustrates
the effect of the
out of range phenomenon:
- Example Program:
(Demo above code)
- Prog file: click here
- The computer can combine
adjacent bytes (memory cells)
and use it as a larger memory cell
Schematically:
A 16 bits memory cell can store one of 216 = 65536 different patterns.
Therefore, it can represent (larger) numbers ranging from: 0 − 65535.
Example: how a computer can use 2 consecutive bytes as a 16 bits memory cell:
The bytes at address 0 and address 1 can be interpreted as a 16 bits memory cell (with address 0)
-
When the computer accesses the
RAM memory,
it specifies:
- The memory location (address)
- The number of bytes it needs
- The computer can also:
- combine
4 consecutive bytes
and use them as
a 32 bits memory cell
- Such a memory call can represent numbers ranging from: 0 − (232-1) or 0 − 4294967295
- combine
8 consecutive bytes
and use them as
a 64 bits memory cell
- Such a memory call can represent numbers ranging from: 0 − (264-1) or 0 − 18446744073709551615
- There is no need (today) to
combine
16 consecutive bytes
and use them as
a 128 bits memory cell
But this may change in the future...
- combine
4 consecutive bytes
and use them as
a 32 bits memory cell