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### A bit about the computer

Bits, bytes, memory and so on

Some 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:
- analogthe numbers represented take on a continuous set of values
- digital thenumbers 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 InformationInterchange

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

- Akilobyte is 1,024 (210) bytes
- approx. one thousand
- A megabyte is 1,048,576 (220) bytes
- approx. one million
- Agigabyte 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

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)

TransistorsThe 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.

Extra slidesDecimal 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).

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.

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.

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.

Decimal Binary (76 1001100)

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

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