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Chapter 3

EECS 1520 Chapter Notes - Chapter 3: Sound, Sigd, Mpeg-2


Department
Electrical Engineering and Computer Science
Course Code
EECS 1520
Professor
Parke Godfrey
Chapter
3

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3.1 Data and Computers
Data: basic values or facts
Information: data that is organized to solve problems
Today, computers are “multimedia”, dealing with vast info categories. Helps to modify many
different types of data into Numbers, Text, Audio, Images and Graphics and Video
All data are stored in “binary digits
Data compression: reducing amount of space to store piece of data
Bandwidth: Number of bits or byes that can be transmitted from one place to another in fixed
amount of time
Compression ratio: size of compressed data / size of original data. Should be between number 0
and 1. Closer to 0, tighter the compression
Lossless Compression: original info is not lost
Lossy compression: some info is lost from compaction
Analog and Digital Data
Computers are finite.
Data can represented in two ways: analog or digital.
Analog: continuous representation, analogous to actual info it represents. Proportional to
continuous, infinite world. Computers cannot work with analog data. Instead we “digitize” data
by breaking into pieces and represent those pieces separately
Digital: discrete representation, breaking info up into separate elements
Why use binary in modern computers? Less expensive and more reliable. Also electronic signals
are far easier to maintain
Digital signals jump sharply between two extremes; behaviour called pulse-code modulation.
Any voltage value above threshold=high value and value below is low value. Digital signal is
“reclocked” to original. As long as it is reclocked before too much degradation, no info is lost.
Binary Representations
To represent 2+, we need multiple bits. 4 combos: 00,01,10 and 11.
If 4+, we need more than two bits. Ex. Three bits can represent 8 things, 4 bits to 16 things, 5 bits
to 32 things…
N bits can be presented as 2^n. every time we increase bits by 1, we DOUBLE
3.2 Representing Numeric Data
National relationship exist between numeric data and binary values
Representing Negative Values
Signed-Magnitude Representation: Number representation in which the sign represents
ordering of the number (- and +) and values represents the magnitude
Problem: there are two representations of zero (+ zero and –zero)
Fixed-Size Numbers
We can represent numbers as integer vales, where half are negative numbers. Sign is determined
by magnitude of number. For ex. If max number of decimal digits is 2, we can let 1 to 49 be
positive number 1 to 49 while 50 to 99 would be negatives values -50 to 1.
For addition, add the numbers together and DISCARD any carry

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For negatives: Negative(I) = 10k I, where k is number of digits
So -3 in two-digit representation would be : −(3) = 102 − 3 = 97
For 3-digit representation: −(3) = 103 − 3 = 997.
Ten’s complement: representation of negative numbers such that negative of I is 10 raised to K
minus I
Since we store everything in modern computer in binary, we use binary equivalent of tens
complement called twos complement
Two’s Complement
To make it easier to look at long binary numbers, we make number line vertical
Ex. −(2) = 27 − 2 = 128 − 2 = −126 ( this is decimal 126, octal 176 and 1111110 in binary)
Leftmost digit shows whether it is positive or negative. 0 is positive and 1 is negative. SO –(2) is
11111110 and negative
Easier way to calculate twos complement: INVERT BITS AND ADD 1. Leftmost bit in negative
number is always 1 so you can tell whether twos complement is negative or positive
Number overflow
Overflow: Occurs when value we compute cannot fit into number of bits we allocated for the
result.
Ex. If each value were stored using eight bits, adding 127 to 3 would produce an overflow.
Representing Real Numbers
Noninteger values=real values. They have whole part and fractional part
The position to right of decimal point would work same way except powers are negative. Ex.
Position to right of decimal point are tenths position (10^-1), the hundredths position (10^-2) and
so on.
In binary, same rule apply except base value is 2. The decimal point is referred to as “radix
point” term used for any base Position to right of radix point in binary are halves position (2^-1)
quarters (2^-2) etc…
How to show real value in computer? We store value as integer and include info of where radix
point is
Real value has 3 properties: sign(+ or -), mantissa (which is made up of digits in value with radix
point assumed to be right) and exponent (determining how radix point is shifted relative to
mantissa.
Example: real value in base 10= _______________________________
Called “floating point” because number of digits is fixed but radix point floats.
When value is floating-point form, positive exponent shift decimal point to right and negative
shifts it to the left.
How to convert real number in decimal notation to floating point notation.
Example: number 148.69 (sign is positive and two digits appear to right)
The exponent is -2 giving us 14869*10^-2.
How to convert floating-point form back to decimal?
Exponent on base tell how many position to move radix point.
If exponent=negative, we move radix point to left
If Positive= we move radix point to the right
Binary floating point value formula=sign*mantissa2^exp

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Floating point number in binary on computer we store 3 values that define it For ex. If we devote
64 bits to storage of floating point value, we use 1 bit for sign, 11 bits for exponent and 52 for
mantissa.
How to change fractional part of decimal to binary?
We multiply by new base rather than dividing. Carry from multiplication becomes next digit to
right in answer. Fractional part of result in than multiplied by new base. Process continues until
fractional part is 0.
Lets convert .75 to binary:
.75 * 2 = 1.50
.50 * 2 = 1.00
Therefore, .75 in decimal is .11 in binary
Lets convert 20.25 in decimal to binary
First we have to convert 20.
20 in binary is 10100. Now convert the fractional part
Therefore, 20.25 in decimal lis 10100.01 in binary.
Scientific Notation: form of floating-point in which decimal point is kept right of leftmost digit.
There is one whole number. For example, 12001.32708 are written as 1.200132708E+4 in
scientific notation.
3.3 Representing Text
Document is continuous (analog) entity and separate characters are discrete (digital) elements
that we represent and store in computer memory.
General approach for representing characters is to list all of them and assign binary string to each
character. For example, particular letter, we store appropriate bit string.
Character set: list of characters and codes used to represent each one.
Two kinds: ASCII and UniCode
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