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Operators & Identifiers. The Data Elements. exponentiation multiplication division ( real ) division ( integer quotient ) division ( integer remainder ) addition Subtraction assignment. ^ * / \ Mod + - =. Arithmetic Operators. Evaluate these expressions.

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Operators identifiers

Operators & Identifiers

The Data Elements


Arithmetic operators

exponentiation

multiplication

division (real)

division (integer quotient)

division (integer remainder)

addition

Subtraction

assignment

^

*

/

\

Mod

+

-

=

Arithmetic Operators








Variables
Variables

  • A variable is a string used to identify a memory location.

  • The amount of memory is determined by the type of data that it will store.

  • Typically, variable names need to be declared so the operating system can allocate sufficient space.

  • Then values of the specified type can be assigned, i.e. stored in that location.


Variable names in vb
Variable Names in VB

  • Must begin with a letter

    • Can include letters and numerals

    • Cannot include spaces

  • Use names that are descriptive

  • Capitalising convention

    • InterestRate, InitialCapital


Variables1
Variables

  • Local

    • Declared within a subprogram

    • Dim varName As dataType

  • Global

    • Declared at the top of the code listing

    • Private varName As dataType




Data storage short type
Data Storage (Short type)

27 26 25 24 23 22 21 20

128 64 32 16 8 4 2 1

1 1 1 1 1 1 1 1

128 +64 +32 +16 +8 +4 + 2 + 1

=255


Data storage 2nd byte
Data Storage (2nd byte)

215 214 213 212 211 210 29 28

32768 16384 8192 4096 2048 1024 512 256

1 1 1 1 1 1 1 1

32768+16384 +8192 +4096 +2048 +1024 +512 +256

=65280

+255

65535

The largest Unsigned value that can be stored in 16 bits.

How many patterns are there?


Integer storage
Integer Storage

  • To store integers, half the combinations are used to represent negative values.

  • The range for Integer type variables is:

    -32,768 to +32767

  • The MSB is used to represent the sign.

  • Which value of the sign bit (0 or 1) will represent a negative number?


2 s complement notation examples in 8 bits to save space
2’s Complement Notation(examples in 8 bits to save space)

  • The notation system that uses 1 to represent negative values.

  • Fixed length notation system.

  • Zero is the first non-negative value:

    00000000

  • The pattern immediately before zero is -1

    11111111

  • The largest value is stored as 01111111

  • The smallest value is stored as 10000000


Arithmetic in 2 s complement remember it s a fixed length system
Arithmetic in 2’s Complement(remember it’s a fixed length system)

00 + 00 = 00

00 + 01 = 01

01 + 00 = 01

01 + 01 = 10


Integer storage 4 bytes
Integer Storage (4 bytes)

  • High order bit (MSB) is worth 231

  • The number of different combinations

    • 232

    • 4,294,967,296

  • Half are used for negative values, so the range is

    • 2,147,483,648 to + 2,147,483,647


  • Long integers
    Long Integers

    • In 8 bytes there are 64 bits!

    • High order bit (MSB) is worth 263.

    • The number of different combinations

      • 264

      • 18,446,744,073,709,650,616


    Fractions
    Fractions

    • A radix separates the integer part from the fraction part of a number.

      101.101

    • Columns to the right of the radix have negative powers of 2.







    Scientific notation
    Scientific Notation

    Very large and very small numbers are often represented such that their order of magnitude can be compared.

    The basic concept is an exponential notation using powers of 10.

    a × 10b

    Where b is an integer, and a is a real number such that:

    1 ≤ |a| < 10


    Scientific notation1
    Scientific Notation

    An electron's mass is about

    0.00000000000000000000000000000091093826 kg.

    In scientific notation, this is written

    9.1093826×10−31 kg.

    The Earth's mass is about

    5,973,600,000,000,000,000,000,000 kg.

    In scientific notation, this is written

    5.9736×1024 kg.


    E notation
    E Notation

    To allow values like this to be expressed on calculators and early terminals

    × 10b

    was replaced by Eb

    So 9.1093826×10−31

    becomes 9.1093826E−31

    And 5.9736×1024

    becomes 5.9736E+24


    E notation1
    E Notation

    The ‘a’ part of the number is called the mantissa or significand.

    The ‘Eb’ part is called the exponent.

    Since these numbers could also be negative they would typically have a sign as well.


    Floating point storage
    Floating Point Storage

    In floating point notation the bit pattern is divided into 3 components:

    Sign– 1 bit (0 for +, 1 for -)

    Exponent– stored in Excess notation

    Mantissa– must begin with 1


    Excess notation examples are in 8 bits to save space
    Excess Notation(examples are in 8 bits to save space)

    • The notation system that uses 0 to represent negative values.

    • Fixed length notation system.

    • Zero is the first non-negative value:

      • 10000000

    • The pattern immediately before zero is -1

      • 01111111

    • The largest value is stored as 11111111

    • The smallest value is stored as 00000000


    Mantissa
    Mantissa

    • Assumes a radix point immediately left of the first digit.

    • The exponent will determine how far and in which direction to move the radix.


    An example in 8 bits
    An example in 8 bits

    If the following pattern stores a floating point value, what is it?

    01101001


    An example in 8 bits1
    An example in 8 bits

    If the following pattern stores a floating point value, what is it?

    01101001

    Separate it into its components:


    An example in 8 bits2
    An example in 8 bits

    If the following pattern stores a floating point value, what is it?

    01101001

    Separate it into its components:signexponentmantissa


    An example in 8 bits3
    An example in 8 bits

    If the following pattern stores a floating point value, what is it?

    01101001

    Separate it into its components:signexponentmantissa


    An example in 8 bits4
    An example in 8 bits

    01101001

    A sign bit of 0 means the number is…?


    An example in 8 bits5
    An example in 8 bits

    01101001

    A sign bit of 0 means the number is positive.

    110 in Excess Notation converts to …?


    An example in 8 bits6
    An example in 8 bits

    01101001

    A sign bit of 0 means the number is positive.

    110 in Excess Notation converts to +2.

    Place the radix in the mantissa …


    An example in 8 bits7
    An example in 8 bits

    01101001

    A sign bit of 0 means the number is positive.

    110 in Excess Notation converts to +2.

    Place the radix in the mantissa .1001

    Put it all together …


    An example in 8 bits8
    An example in 8 bits

    01101001

    A sign bit of 0 means the number is positive.

    110 in Excess Notation converts to +2.

    Place the radix in the mantissa .1001

    Put it all together …

    +.1001 * 22


    An example in 8 bits9
    An example in 8 bits

    +.1001 * 22

    Multiplying a binary number by 2 shifts the bits left (move the radix to the right) one position.

    So the exponent tells us to shift the radix 2 positions right.

    +10.01

    = 2¼


    Normal form
    Normal Form

    • The first bit of the mantissa must be 1 to prevent multiple representations of the same value.



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