A bit about the computer

Bits, bytes, memory and so onSome of this material can be found in

Discovering Computers 2000 (Shelly, Cashman and Vermaat) 3.11-3.13 and the

appendix A.1-A.4.

A computer is

a person or thing that computes to compute is to determine by arithmetic

means (The Randomhouse Dictionary) so computing involves numbers While typing papers, drawing pictures

and surfing the Net don’t seem to involve numbers at first, numbers are lurking beneath the surface

Representing numbers

Some attribute of the computer is used to “represent” numbers (for example: a child’s fingers)

two kinds of representation are:– analog the numbers represented take on a

continuous set of values

– digital the numbers represented take on a discrete set of values

Pros and Cons

the analog representation is fuller/richer after all there are an infinite number of values available

the digital representation is safer from corruption by “noise;” there is a big difference between the various discrete values, and smaller, more subtle differences do not affect the representation

Our computers are

digital and electronic

(note that digital electronic)

they are electronic because they use an electronic means (e.g. voltage or current) to represent numbers

they are digital because the numbers represented are discrete

Binary representation

the easiest distinction to make is between

– low and high voltage

– off and on

then we can only represent two digits: 0 and 1

but we can represent any (whole) number using 0’s and 1’s

Decimal vs. Binary

Decimal (base 10)

– 124 = 100 + 20 + 4

– 124 = 1 102 + 2 101 + 4 100

Binary (base 2)

– 1111100 = 64 + 32 + 16 + 8 + 4 + 0 + 0

– 1111100 = 1 26 + 1 25 + 1 24 + 1 23

+ 1 22 + 0 21 + 0 20

Bits and Bytes

A bit is a single binary digit (0 or 1).

A byte is a group of eight bits.

A byte can be in 256 (28) distinct states (which we might choose to represent the numbers 0 through 255).

Note computer scientists like to start counting with zero.

Realizing a bit

We need two “states,” e.g.

– high or low voltage (e.g. computer chips)

• why you should protect computer from power surges

– north or south pole of a magnet (e.g. floppy disks)

• why you should keep floppies away from large magnets

– light or dark (e.g. CD)

– hole or no hole (e.g. punch card or CD)

Representing characters

Combinations of 0’s and 1’s can be used to represent characters

This is most commonly done using ASCII code

American Standard Code for

Information Interchange

ASCII code (a byte per character)

0 00110000 8 00111000 G 01000111

1 00110001 9 00111001 H 01001000

2 00110010 A 01000001 I 01001001

3 00110011 B 01000010 J 01001010

4 00110100 C 01000011 K 01001011

5 00110101 D 01000100 L 01001100

6 00110110 E 01000101 M 01001101

7 00110111 F 01000110 N 01001110

More, more, more

A kilobyte is 1,024 (210) bytes – approx. one thousand

A megabyte is 1,048,576 (220) bytes– approx. one million

A gigabyte is 1,073,741,824 (230) bytes – approx. one billion

A terabyte is 1,099,511,627,776 (240) bytes– approx. one trillion

Storing it away

A standard 3.5 inch floppy disk holds 1.44 MB (megabytes)

An Iomega Zip disk holds approx. 100 MB – (the computers in Olney 200 have zip drives)

A CD holds approx. 600 MB

A typical hard drive holds a few GB (gigabytes)

Storing the Starr report

The report plus supporting material

If there were:

– 60 characters per line

– 66 lines per page (single spaced)

– 500 pages in a ream of paper

– 10 reams in a box

– and 18 boxes

The Grand Total

N = 60 66 500 10 18

N = 356,400,000

N 340 MB (megabytes)

The Starr report and the accompanying materials would fit on a few zip disks or one writable CD.

True or False

A boolean expression is a condition that is either true or false (on or off)

Logical operators:

– like an arithmetic operator (e.g. addition) that takes in two numbers (operands) and yields a number as a result (1+1=2)

– Logical operators take in two boolean expressions and produces a boolean outcome

AND

Bit 1 Bit 2 (Bit 1 AND Bit 2)

0 (false) 0 (false) 0 (false)

0 (false) 1 (true) 0 (false)

1 (true) 0 (false) 0 (false)

1 (true) 1 (true) 1 (true)

use to narrow searches

Example of “AND”

“Mark McGwire” AND supplement

McGwire’s use of Androstenedione

OR

use to widen searches

Bit 1 Bit 2 (Bit 1 OR Bit 2)

0 (false) 0 (false) 0 (false)

0 (false) 1 (true) 1 (true)

1 (true) 0 (false) 1 (true)

1 (true) 1 (true) 1 (true)

Example of “OR”

“Mark McGwire” OR “Sammy Sosa”

Either McGwire or Sosa or both

Transistors

When bits are represented using voltage, the logical operators (gates) can be constructed from transistors

The Pentium ® II has approximately 7.5 million transistors on it

The transistors have lengths approximately 0.35 microns (millionths of a meter)

Extra slides

The following slides are on converting numbers from decimal to binary

Don’t panic. I never ask this on tests.

I just like to expose people to it.

Decimal Binary

Take the decimal number 76

Look for the largest power of 2 that is less than 76.

The powers of 2 are 1, 2, 4, 8, 16, 32, 64, 128, 256, etc.

So the largest power of 2 less than 76 is 64=26.

Decimal Binary (76 1001100)

Put a 1 on the 26’s place, and subtract 64 from 76 leaving 12.

Ask if the next lower power of 2, 32=25 is greater than or less than or equal to what we have left (12).

26 25 24 23 22 21 20

1

Decimal Binary (76 1001100)

32 is greater than 12 so we put a 0 in the 25’s place.

16 is greater than 12 so we put a 0 in the 24’s place.

26 25 24 23 22 21 20

1 0

Decimal Binary (76 1001100)

8 is less than 12, so we put a 1 in the 23’s place, and subtract 8 from 12 leaving 4.

26 25 24 23 22 21 20

1 0 0 1

26 25 24 23 22 21 20

1 0 0

Decimal Binary (76 1001100)

4 is equal to 4, so we put a 1 in the 22’s place, and subtract 4 from 4 leaving 0.

2 is greater than 0 so we put a 0 in the 21’s place.

26 25 24 23 22 21 20

1 0 0 1 1

Decimal Binary (76 1001100)

1 is greater than 0 so we put a 0 in the 20’s place.

26 25 24 23 22 21 20

1 0 0 1 1 0 0

26 25 24 23 22 21 20

1 0 0 1 1 0