Introduction to Computer Lesson 7.0

Introduction to Computer Lesson VII

By: Vhonz SugatanPOWER School

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Number System

Number System

Decimal to Binary Conversion of Fraction

Number System

Decimal to Binary Conversion of Real Values

Number System

Binary to Decimal Conversion of Real Values

Number System

Binary Addition

Number SystemBinary Subtraction


0 - 0 =


0 - 0 = 0


0 - 0 = 01 - 0 =


0 - 0 = 01 - 0 = 1


0 - 0 = 01 - 0 = 11 - 1 =


0 - 0 = 01 - 0 = 11 - 1 = 0


0 - 0 = 01 - 0 = 11 - 1 = 00 - 1 =


0 - 0 = 01 - 0 = 11 - 1 = 00 - 1 = 0


0 - 0 = 01 - 0 = 11 - 1 = 00 - 1 = 0 With a borrow of 1

Number SystemExample:


1010


1010100


1010100

0


1010100

10


1010100

10

2


1010100110

2


1010100110

20


1010


1010101


1010101101


1000111111


1000111111

10100


1000.1111.01


1000.1111.01

101.10


100001111


100001111

1

Number SystemThe One’s Compliment Method


11010


11010 is 00101


111101


111101000010


110011(Base2)


110011(Base2)

11101(Base2)

Number SystemStep 1:

Number SystemStep 1:Get the one’s compliment of subtrahend

Number SystemStep 1:Get the one’s compliment of subtrahend.

The one’s compliment of 11101is 00010

Number SystemStep 2:Get the binary sum of the minuend and the one’s compliment of the subtrahend.

Number SystemStep 2:Get the binary sum of the minuend and the one’s compliment of the subtrahend.

110011 + 00010 = 110101

Number SystemStep 3:Add the and-around carry by taking the leftmost digit of the binary sum and adding it with the first digit.


110101


101011+


101011+

10110

Number SystemBinary Multiplication


0 x 0 =


0 x 0 = 0


0 x 0 = 01 x 0 =


0 x 0 = 01 x 0 = 0


0 x 0 = 01 x 0 = 00 x 1 =


0 x 0 = 01 x 0 = 00 x 1 = 0


0 x 0 = 01 x 0 = 00 x 1 = 01 x 1 =


0 x 0 = 01 x 0 = 00 x 1 = 01 x 1 = 1

Number SystemExample

Number SystemExample 111


101x


101x111


101x111

000


101x111

000111


101x111

000111+


101x111

000111+

100011


101x


101x101


101x101

000


101x101

000101


101x101

000101+


101x101

000101+11001

Number SystemExample 11.00


10.10x


10.10x00 00


10.10x00 00

110 0


10.10x00 00

110 00000


10.10x00 00

110 00000

1100


10.10x00 00

110 00000

1100+


10.10x00 00

110 00000

1100+

1111000


10.10x00 00

110 00000

1100+

111.1000

Number SystemBinary Division


0 / 1 =


0 / 1 = 0


0 / 1 = 01 / 1 =


0 / 1 = 01 / 1 = 1


0 / 1 = 01 / 1 = 11 / 0 =


0 / 1 = 01 / 1 = 11 / 0 = is undefined


100 1100


100 11001


100 11001

100


100 11001

100-


100 11001

100-10


100 11001

100-100


100 110011

100-100


100 110011

100-100100


100 110011

100-100100-


100 110011

100-100100-000

Number System

The Octal Number System

Number SystemDecimal to Octal Conversion

Number SystemDecimal to Octal ConversionExample:

Convert 56(base 10) to its octal equivalent.


Division Quotients Remainders56 / 8


Division Quotients Remainders56 / 8 7


Division Quotients Remainders56 / 8 7 0


Division Quotients Remainders56 / 8 7 07 / 8


Division Quotients Remainders56 / 8 7 07 / 8 0


Division Quotients Remainders56 / 8 7 07 / 8 0 7


56(base 10) is equivalent to 70(base8)


5687

560


8 7


8 7.0


8 7.00.


8 7.00.8


8 7.00.8

64


8 7.00.8

64

6


8 7.000.8

64

60


8 7.000.87

64

60


8 7.000.87

64

6056


8 7.000.87

64

6056

4


8 7.0000.87

64

6056

40


8 7.0000.875

64

6056

40


8 7.0000.875

64

6056

4040


8 7.0000.875

64

6056

4040

0

Number SystemDecimal to Octal ConversionSeat Work

Number SystemDecimal to Octal ConversionSeat Work

1.) 171 base10 to base82.) 1254 base10 to base83.) 1573 base10 to base8

Number SystemOctal to Decimal Conversion

Number SystemOctal to Decimal ConversionExample:

Convert 70(base 8) to its decimal equivalent.

Number SystemOctal to Decimal ConversionExample:70 base8

7 0


7 0x8 x8


7 0x8 x8+


7 0x8 x8+01


7 0x8 x8+01

0


7 0x8 x8+01

056


7 0x8 x8+01

56 + 0


7 0x8 x8+01

56 +56

0


Convert 36471(base 8) to its decimal equivalent.


3x8+6x8+4x8+7x8+1x801234


3x8+6x8+4x8+7x8+1x801234

1


3x8+6x8+4x8+7x8+1x801234

156


3x8+6x8+4x8+7x8+1x801234

156256


3x8+6x8+4x8+7x8+1x801234

1562563072


3x8+6x8+4x8+7x8+1x801234

156256307212288


3x8+6x8+4x8+7x8+1x801234

156256307212288 ++++


3x8+6x8+4x8+7x8+1x801234

156256307212288 ++++

= 15673

Number SystemOctal to Binary Conversion

Number SystemOctal to Binary ConversionOCTAL

NUMBERBINARY

EQUIVALENT

0 000

1 001

2 010

3 011

4 100

5 101

6 110

7 111

Number SystemOctal to Binary ConversionExample:


Convert 13(base 8) to its binary equivalent.


1 (base8) in binary is equal to 001


1 (base8) in binary is equal to 001 3 (base8) in binary is equal to 011


1 (base8) in binary is equal to 001 3 (base8) in binary is equal to 011 Therefore 13 (base8) is equal

to 001011 or 1011


Convert 765(base 8) to its binary equivalent.


7 (base8) to binary is 111


7 (base8) to binary is 111 6 (base8) to binary is 110


7 (base8) to binary is 111 6 (base8) to binary is 110 5 (base8) to binary is 101


7 (base8) to binary is 111 6 (base8) to binary is 110 5 (base8) to binary is 101

Therefore 765 (base8) is equal to 111110101

Number SystemBinary to Octal Conversion

Number SystemBinary to Octal ConversionExample:

Convert 10101010(base2) to its octal equivalent.

Number SystemBinary to Octal ConversionStep 1:

Arrange the binary into groups of 3.


Arrange the binary into groups of 3.

10101010


For each group, convert each digit to decimal by multiplying it by its positional value.

Number SystemBinary to Octal ConversionStep 2:GROUP CONVERSION TO OCTAL

010 0x2+1x2+0x2 = 2101 1x2+0x2+1x2 = 510 1x2+0x2 = 2

Number SystemBinary to Octal Conversion

Therefore the 10101010 (base2) is equivalent to 252 (base8)

Number System

The Hexadecimal

Number System

Introduction to Computer Lesson 7.0

Devices & Hardware

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