Post on 14-Aug-2015
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
Number SystemBinary Subtraction
0 - 0 =
Number SystemBinary Subtraction
0 - 0 = 0
Number SystemBinary Subtraction
0 - 0 = 01 - 0 =
Number SystemBinary Subtraction
0 - 0 = 01 - 0 = 1
Number SystemBinary Subtraction
0 - 0 = 01 - 0 = 11 - 1 =
Number SystemBinary Subtraction
0 - 0 = 01 - 0 = 11 - 1 = 0
Number SystemBinary Subtraction
0 - 0 = 01 - 0 = 11 - 1 = 00 - 1 =
Number SystemBinary Subtraction
0 - 0 = 01 - 0 = 11 - 1 = 00 - 1 = 0
Number SystemBinary Subtraction
0 - 0 = 01 - 0 = 11 - 1 = 00 - 1 = 0 With a borrow of 1
Number SystemExample:
Number SystemExample:
1010
Number SystemExample:
1010100
Number SystemExample:
1010100
Number SystemExample:
1010100
Number SystemExample:
1010100
0
Number SystemExample:
1010100
0
Number SystemExample:
1010100
0
Number SystemExample:
1010100
10
Number SystemExample:
1010100
10
Number SystemExample:
1010100
10
Number SystemExample:
1010100
10
Number SystemExample:
1010100
10
2
Number SystemExample:
1010100110
2
Number SystemExample:
1010100110
20
Number SystemExample:
1010
Number SystemExample:
1010101
Number SystemExample:
1010101101
Number SystemExample:
1000111111
Number SystemExample:
1000111111
10100
Number SystemExample:
1000.1111.01
Number SystemExample:
1000.1111.01
101.10
Number SystemExample:
100001111
Number SystemExample:
100001111
1
Number SystemThe One’s Compliment Method
Number SystemThe One’s Compliment Method
11010
Number SystemThe One’s Compliment Method
11010 is 00101
Number SystemThe One’s Compliment Method
111101
Number SystemThe One’s Compliment Method
111101000010
Number SystemExample:
110011(Base2)
Number SystemExample:
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:
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:
Number SystemStep 3:Add the and-around carry by taking the leftmost digit of the binary sum and adding it with the first digit.
Number SystemStep 3:
110101
Number SystemStep 3:
110101
Number SystemStep 3:
101011+
Number SystemStep 3:
101011+
10110
Number SystemStep 3:
101011+
10110
Number SystemBinary Multiplication
Number SystemBinary Multiplication
0 x 0 =
Number SystemBinary Multiplication
0 x 0 = 0
Number SystemBinary Multiplication
0 x 0 = 01 x 0 =
Number SystemBinary Multiplication
0 x 0 = 01 x 0 = 0
Number SystemBinary Multiplication
0 x 0 = 01 x 0 = 00 x 1 =
Number SystemBinary Multiplication
0 x 0 = 01 x 0 = 00 x 1 = 0
Number SystemBinary Multiplication
0 x 0 = 01 x 0 = 00 x 1 = 01 x 1 =
Number SystemBinary Multiplication
0 x 0 = 01 x 0 = 00 x 1 = 01 x 1 = 1
Number SystemExample
Number SystemExample 111
Number SystemExample 111
101x
Number SystemExample 111
101x111
Number SystemExample 111
101x111
000
Number SystemExample 111
101x111
000111
Number SystemExample 111
101x111
000111+
Number SystemExample 111
101x111
000111+
100011
Number SystemExample 101
Number SystemExample 101
101x
Number SystemExample 101
101x101
Number SystemExample 101
101x101
000
Number SystemExample 101
101x101
000101
Number SystemExample 101
101x101
000101+
Number SystemExample 101
101x101
000101+11001
Number SystemExample 11.00
Number SystemExample 11.00
10.10x
Number SystemExample 11.00
10.10x00 00
Number SystemExample 11.00
10.10x00 00
110 0
Number SystemExample 11.00
10.10x00 00
110 00000
Number SystemExample 11.00
10.10x00 00
110 00000
1100
Number SystemExample 11.00
10.10x00 00
110 00000
1100+
Number SystemExample 11.00
10.10x00 00
110 00000
1100+
1111000
Number SystemExample 11.00
10.10x00 00
110 00000
1100+
111.1000
Number SystemBinary Division
Number SystemBinary Division
0 / 1 =
Number SystemBinary Division
0 / 1 = 0
Number SystemBinary Division
0 / 1 = 01 / 1 =
Number SystemBinary Division
0 / 1 = 01 / 1 = 1
Number SystemBinary Division
0 / 1 = 01 / 1 = 11 / 0 =
Number SystemBinary Division
0 / 1 = 01 / 1 = 11 / 0 = is undefined
Number SystemExample
100 1100
Number SystemExample
100 1100
Number SystemExample
100 1100
Number SystemExample
100 1100
Number SystemExample
100 11001
Number SystemExample
100 11001
100
Number SystemExample
100 11001
100-
Number SystemExample
100 11001
100-10
Number SystemExample
100 11001
100-100
Number SystemExample
100 110011
100-100
Number SystemExample
100 110011
100-100100
Number SystemExample
100 110011
100-100100-
Number SystemExample
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.
Number SystemDecimal to Octal ConversionExample:
Division Quotients Remainders56 / 8
Number SystemDecimal to Octal ConversionExample:
Division Quotients Remainders56 / 8 7
Number SystemDecimal to Octal ConversionExample:
Division Quotients Remainders56 / 8 7 0
Number SystemDecimal to Octal ConversionExample:
Division Quotients Remainders56 / 8 7 07 / 8
Number SystemDecimal to Octal ConversionExample:
Division Quotients Remainders56 / 8 7 07 / 8 0
Number SystemDecimal to Octal ConversionExample:
Division Quotients Remainders56 / 8 7 07 / 8 0 7
Number SystemDecimal to Octal ConversionExample:
Division Quotients Remainders56 / 8 7 07 / 8 0 7
Number SystemDecimal to Octal ConversionExample:
56(base 10) is equivalent to 70(base8)
Number SystemDecimal to Octal Conversion
5687
560
Number SystemDecimal to Octal Conversion
8 7
Number SystemDecimal to Octal Conversion
8 7.0
Number SystemDecimal to Octal Conversion
8 7.00.
Number SystemDecimal to Octal Conversion
8 7.00.8
Number SystemDecimal to Octal Conversion
8 7.00.8
64
Number SystemDecimal to Octal Conversion
8 7.00.8
64
Number SystemDecimal to Octal Conversion
8 7.00.8
64
6
Number SystemDecimal to Octal Conversion
8 7.000.8
64
60
Number SystemDecimal to Octal Conversion
8 7.000.87
64
60
Number SystemDecimal to Octal Conversion
8 7.000.87
64
6056
Number SystemDecimal to Octal Conversion
8 7.000.87
64
6056
Number SystemDecimal to Octal Conversion
8 7.000.87
64
6056
4
Number SystemDecimal to Octal Conversion
8 7.0000.87
64
6056
40
Number SystemDecimal to Octal Conversion
8 7.0000.875
64
6056
40
Number SystemDecimal to Octal Conversion
8 7.0000.875
64
6056
4040
Number SystemDecimal to Octal Conversion
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
Number SystemOctal to Decimal ConversionExample:70 base8
7 0x8 x8
Number SystemOctal to Decimal ConversionExample:70 base8
7 0x8 x8+
Number SystemOctal to Decimal ConversionExample:70 base8
7 0x8 x8+01
Number SystemOctal to Decimal ConversionExample:70 base8
7 0x8 x8+01
0
Number SystemOctal to Decimal ConversionExample:70 base8
7 0x8 x8+01
056
Number SystemOctal to Decimal ConversionExample:70 base8
7 0x8 x8+01
56 + 0
Number SystemOctal to Decimal ConversionExample:70 base8
7 0x8 x8+01
56 +56
0
Number SystemOctal to Decimal ConversionExample:
Convert 36471(base 8) to its decimal equivalent.
Number SystemOctal to Decimal ConversionExample:
3x8+6x8+4x8+7x8+1x801234
Number SystemOctal to Decimal ConversionExample:
3x8+6x8+4x8+7x8+1x801234
1
Number SystemOctal to Decimal ConversionExample:
3x8+6x8+4x8+7x8+1x801234
156
Number SystemOctal to Decimal ConversionExample:
3x8+6x8+4x8+7x8+1x801234
156256
Number SystemOctal to Decimal ConversionExample:
3x8+6x8+4x8+7x8+1x801234
1562563072
Number SystemOctal to Decimal ConversionExample:
3x8+6x8+4x8+7x8+1x801234
156256307212288
Number SystemOctal to Decimal ConversionExample:
3x8+6x8+4x8+7x8+1x801234
156256307212288 ++++
Number SystemOctal to Decimal ConversionExample:
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:
Number SystemOctal to Binary ConversionExample:
Convert 13(base 8) to its binary equivalent.
Number SystemOctal to Binary ConversionExample:
1 (base8) in binary is equal to 001
Number SystemOctal to Binary ConversionExample:
1 (base8) in binary is equal to 001 3 (base8) in binary is equal to 011
Number SystemOctal to Binary ConversionExample:
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
Number SystemOctal to Binary ConversionExample:
Convert 765(base 8) to its binary equivalent.
Number SystemOctal to Binary ConversionExample:
7 (base8) to binary is 111
Number SystemOctal to Binary ConversionExample:
7 (base8) to binary is 111 6 (base8) to binary is 110
Number SystemOctal to Binary ConversionExample:
7 (base8) to binary is 111 6 (base8) to binary is 110 5 (base8) to binary is 101
Number SystemOctal to Binary ConversionExample:
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.
Number SystemBinary to Octal ConversionStep 1:
Arrange the binary into groups of 3.
10101010
Number SystemBinary to Octal ConversionStep 1:
Arrange the binary into groups of 3.
10101010
Number SystemBinary to Octal ConversionStep 2:
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 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