Data Storage – Part 1 CS 1 Introduction to Computers and Computer Technology Rick Graziani Fall 2013

Data Storage – Part 1

CS 1 Introduction to Computers and Computer Technology

Rick Graziani

Fall 2013

Rick Graziani [email protected] 2

BIT – BInary digiT

• Bit (Binary Digit) = Basic unit of information, representing one of two discrete states. The smallest unit of information within the computer.

• The only thing a computer understands.• Abbreviation: b• Bit has one of two values:

– 0 (off) or 1 (on)– 0 (False) or 1 (True)

OFF ON


Bits

• Two patterns are known as the state of the bit.

• For example, magnetic encoding of information on tapes, floppy disks, and hard disks are done with positive or negative polarity.

The boxes illustrate a position where magnetism may be set and sensed; pluses (red) indicate magnetism of positive polarity (1 bit), interpreted as “present” and minuses (blue) (0 bit).

0 0 0 0 0 0 0 01 1 1 1 1 1 1 1


Bits

• Bits are really only symbols.• Used to display the one of two different, discrete states.• Bits are used as:

– Storing data • Numbers• Text characters• Images• Sound• Etc.

– Processing data


Boolean Operations

• Integrated Circuits (microchips) are used to store and manipulate (process) bits.

• This is done using Boolean operations (in honor of mathematician George Boole, 1815-1864).

• Boolean Operation: An operation that manipulates one or more true/false values

• Specific operations– AND– OR– XOR (exclusive or)– NOT

• Using Truth Tables we can uses different sets of logic operations to store, add, subtract, and more complicated operations with bit.

Boolean Algebra and logical expressions (Addendum)

• Boolean algebra (due to George Boole) - The mathematics of digital logic – Useful in dealing with binary system of numbers. – Used in the analysis and synthesis of logical expressions.

• Logical expressions – Expressions constructed using logical-variables and operators. – Result is: True or False

• Boolean algebra – In mathematics a variable uses one of the two possible values: 1 or 0

• May also be represented as:– Truth or Falsehood of a statement – On or Off states of a switch – High (5V) or low (0V) of a voltage level


Used in electronics (Addendum)

• Electrical circuits are designed to represent logical expressions – Known as logic circuits.

• Used to make important logical decisions in household appliances, computers, communication devices, traffic signals and microprocessors.

• Three basic logic operations as listed below: – OR operation – AND operation – NOT operation

• A logic gate is an electronic circuit/device which makes the logical decisions based on these operations.


Logic gates (Addendum)

• Logic gates have: – one or more inputs – only one output

• The output is active only for certain input combinations.

• Logic gates are the building blocks of any digital circuit.



Boolean Operations - AND

• Truth tables (simple ones)

• AND operation– Both input values must be TRUE for output to be TRUE– Kermit is a frog AND Miss Piggy is an actress– Inputs to AND operation represent truth of falseness of the

compound statement.

AND = TRUE

TRUE TRUE


Boolean Operations

• Gate: – A device that computes a Boolean operation – A device that produces the output of a Boolean operation when given

the operation’s input values.• Gates can be:

– Gears– Relays– Optic devices– Electronic circuits (microchips)


Boolean Operations – AND Gate

0 = FALSE

1 = TRUE

AND operation

• Both input values must be TRUE for output to be TRUE

0

00

Truth Table

Inputs Output

0 0

0 1

1 0

1 1

00

10 0

1

00

0

1

11

1


Boolean Operations - OR

• Truth tables (simple ones)

• OR operation– Only one input values must be TRUE for output to be TRUE– In Rick likes to surf OR Rick likes to go dancing.– Taking both courses will also TRUE.

OR = TRUETRUE True


Boolean Operations – OR Gate

0 = FALSE

1 = TRUE

OR operation

• At least one input value must be TRUE for output to be TRUE

0

00

Truth Table

Inputs Output

0 0

0 1

1 0

1 1

00

11 1

1

01

1

1

11

1


Boolean Operations - XOR

• Truth tables (simple ones)• XOR operation

– One and ONLY one input value can be TRUE for output to be TRUE

– At noon Rick is going to surf the Hook XOR surf Liquor Stores (this is a surf spot)

– Both cannot be true, as I cannot surf both spots at the same time.

XOR = TRUETRUE False


Boolean Operations – XOR Gate

0 = FALSE

1 = TRUE

XOR operation

• Only one input value is TRUE for output to be TRUE

Truth Table

Inputs Output

0 0

0 1

1 0

1 1

0

00

00

11 1

1

01

1

1

10

0


Boolean Operations – NOT Gate

0 = FALSE

1 = TRUE

NOT operation

• Only one input

• Opposite of input

NOT FALSE = TRUE

NOT TRUE = FALSE

Truth Table

Inputs Output

0

1

0 1

1

1 0 0

http://www.cs.kent.edu/~volkert/F10-10051/notes/logsim.html



Another way to write it…

0 = FALSE; 1 = TRUE


Binary Math


Base 10 (Decimal) Number System

Digits (10): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Number of:

104 103 102 101 100

10,000’s 1,000’s 100’s 10’s 1’s

1

2

3

9

1 0

9 9

1 0 0


Base 10 (Decimal) Number System

Digits (10): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Number of:

104 103 102 101 100

10,000’s 1,000’s 100’s 10’s 1’s

4 1 0 8

3 8 2

1 0 0 0 9

1 0 0 1 0


Rick’s Number System Rules

• All digits start with 0

• A Base-n number system has n number of digits:– Decimal: Base-10 has 10 digits– Binary: Base-2 has 2 digits– Hexadecimal: Base-16 has 16 digits

• The first column is always the number of 1’s

• Each of the following columns is n times the previous column (n = Base-n)– Base 10: 10,000 1,000 100 10 1– Base 2: 16 8 4 2 1 – Base 16: 65,536 4,096 256 16 1


Counting in Decimal (0,1,2,3,4,5,6,7,8,9)

1,000’s 100’s 10’s 1’s0123

...9

1 01 1

...1 81 92 02 12 2

1,000’s 100’s 10’s 1’s. . .2 93 03 1

...9 9

1 0 01 0 1

...9 9 9

1 0 0 0


Counting in Binary (0, 1)

8’s 4’s 2’s 1’s01

1 01 1

1 0 01 0 1

8’s 4’s 2’s 1’s

1 1 0

1 1 1

1 0 0 0

1 0 0 1

1 0 1 0

1 0 1 1

1 1 0 0

1 1 0 1

1 1 1 0

1 1 1 1

Dec Dec

0123456

7

8

9

10

11

12

13

14

15


Binary Math (more later)

0 0 1 10 11 100 101

+0 +1 +1 +1 +1 + 1 + 1

0 1 10 11 100 101 110

111 00000000 11111110

+ 1 + 0 -> + 1

1000 …… 00000000 11111111


Base 2 (Binary) Number System

Digits (2): 0, 1

Number of:

27 26 25 24 23 22 21 20

128’s 64’s 32’s 16’s 8’s 4’s 2’s 1’s

Dec.

2 1 0

10 1 0 1 0

17

70

130

255


Base 2 (Binary) Number System

Digits (2): 0, 1

Number of:

27 26 25 24 23 22 21 20

128’s 64’s 32’s 16’s 8’s 4’s 2’s 1’s

Dec.

2 1 0

10 1 0 1 0

17 1 0 0 0 1

70 1 0 0 0 1 1 0

130 1 0 0 0 0 0 1 0

255 1 1 1 1 1 1 1 1


Converting between Decimal and Binary

Digits (2): 0, 1

Number of:

27 26 25 24 23 22 21 20

128’s 64’s 32’s 16’s 8’s 4’s 2’s 1’s

Dec.

1 0 0 0 1 1 0

1 0 1 0 0 0

0 0 0 0 0 0 0 0

1 0 0 0 0 0 0 0

172

192


Converting between Decimal and Binary

Digits (2): 0, 1

Number of:

27 26 25 24 23 22 21 20

128’s 64’s 32’s 16’s 8’s 4’s 2’s 1’s

Dec.

70 1 0 0 0 1 1 0

40 1 0 1 0 0 0

0 0 0 0 0 0 0 0 0

128 1 0 0 0 0 0 0 0

172 1 0 1 0 1 1 0 0

192 1 1 0 0 0 0 0 0


Computers do Binary

0 1• Bits have two values: OFF and ON

• The Binary number system (Base-2) can represent OFF and ON very well since it has two values, 0 and 1– 0 = OFF– 1 = ON

• Understanding Binary to Decimal conversion is critical in computer science, computer networking, digital media, etc.


Rick’s Program


Rick’s Program


Rick’s Program


Decimal Math - Addition

10,000’s 1,000’s 100’s 10’s 1’s

1 6 5 1 0

+ 1 6 5 9 5

-----------------------------50

1

13

1

3

1


Binary Math - Addition

64’s 32’s 16’s 8’s 4’s 2’s 1’s

1 1 1 0 1 0

+ 1 1 0 1 1

-----------------------------10

1

10

1

1

1

0

1

1

Double check using Decimal.

Dec

58

27+-----85


Half Adder Gate – Adding two bits

Inputs: A, B

S = Sum

C = Carry

AND

XOR

A + B = 2’s 1’s



Inputs: A, B

S = Sum

C = Carry

AND

XOR

A + B = 2’s 1’s

0 0 =

00

00

SC

0

0

0

+ 0

----0



Inputs: A, B

S = Sum

C = Carry

AND

XOR

A + B = 2’s 1’s

0 1 =

01

10

SC

1

0

0

+ 1

----1



Inputs: A, B

S = Sum

C = Carry

AND

XOR

A + B = 2’s 1’s

1 0 =

10

10

SC

1

0

1

+ 0

----1



Inputs: A, B

S = Sum

C = Carry

AND

XOR

A + B = 2’s 1’s

1 1 =

11

01

SC

0

1

1

+ 1

----1 0


Marble Adding Machine

• http://www.youtube.com/watch?v=GcDshWmhF4A&NR=1&feature=fvwp


Flip-flops

• Flip-flop: A circuit built from gates that can store one bit, uses feedback.• A means of storing bits such as RAM• Modern computers use technologies with:

– greater miniaturization – faster response times– additional circuitry

• DRAM (Dynamic RAM)• SDRAM (Synchronous DRAM)• PCs currently use DDR (double data rate) for RAM, DDR1, DDR2 and DDR3

– Type of SDRAM– Each type has types of DIMM (dual in-line memory module) slots

(different number of pins)


Example of Flip Flops storing bits (FYI)

• S = Set

• R = Reset

• DRAM (Dynamic RAM)

– Each bit of data is stored in a separate capacitor within an integrated circuit.

– Since real capacitors leak charge, the information eventually fades unless the capacitor charge is refreshed periodically.


Types of RAM

• Understanding RAM Types: DRAM, SDRAM, DIMM, SIMM & More – http://proprofs.com/mwiki/index.php?

title=Understanding_RAM_Types:_DRAM_SDRAM_DIMM_SIMM_And_More• RAM - From Wikipedia, the free encyclopedia

– http://en.wikipedia.org/wiki/RAM• DDR2 SDRAM - From Wikipedia, the free encyclopedia

– http://en.wikipedia.org/wiki/DDR2_SDRAM• Dynamic random access memory - From Wikipedia, the free encyclopedia

– http://en.wikipedia.org/wiki/Dynamic_random_access_memory

Data Storage – Part 1

CS 1 Introduction to Computers and Computer Technology

Rick Graziani

Documents

Data Storage – Part 1 CS 1 Introduction to Computers and Computer Technology Rick Graziani Fall 2013