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# Number-Systems Notes | EduRev

## : Number-Systems Notes | EduRev

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Number Systems
• Stone Age: knots, some stone marks
• Roman Empire: more systematic notation  I,
II, III, IV, V, VI, VII.VIII, IX, X, C=100,
D=500, M=1000, L=50
• Concept of zero by
– Maya- I century, Hindu-V century
• Positional-value systems: decimal, binary,
octal, etc..
Page 2

Number Systems
• Stone Age: knots, some stone marks
• Roman Empire: more systematic notation  I,
II, III, IV, V, VI, VII.VIII, IX, X, C=100,
D=500, M=1000, L=50
• Concept of zero by
– Maya- I century, Hindu-V century
• Positional-value systems: decimal, binary,
octal, etc..
Positional-Value System
• The value of a digit (“digit” from Latin word
for finger) depends on its position
5  6  7  .  9  1  4
MSD      Decimal     LSD
point
Positional values      2    1    0        -1    -2    -3
(weights)               10 10 10     10  10 10
We will write ( 5 6 7. 9 1 4)
10
Page 3

Number Systems
• Stone Age: knots, some stone marks
• Roman Empire: more systematic notation  I,
II, III, IV, V, VI, VII.VIII, IX, X, C=100,
D=500, M=1000, L=50
• Concept of zero by
– Maya- I century, Hindu-V century
• Positional-value systems: decimal, binary,
octal, etc..
Positional-Value System
• The value of a digit (“digit” from Latin word
for finger) depends on its position
5  6  7  .  9  1  4
MSD      Decimal     LSD
point
Positional values      2    1    0        -1    -2    -3
(weights)               10 10 10     10  10 10
We will write ( 5 6 7. 9 1 4)
10
Binary:
Base-2 Number System
1   0   1   1   1   1  .   0   0   1
2   2    2    2    2    2       2    2    2
5   4   3    2    1    0       -1   -2   -3
We write:  ( 1 0 1 1 1 1 . 0 0 1 )
2
base point or radix
Digits are called bits
Page 4

Number Systems
• Stone Age: knots, some stone marks
• Roman Empire: more systematic notation  I,
II, III, IV, V, VI, VII.VIII, IX, X, C=100,
D=500, M=1000, L=50
• Concept of zero by
– Maya- I century, Hindu-V century
• Positional-value systems: decimal, binary,
octal, etc..
Positional-Value System
• The value of a digit (“digit” from Latin word
for finger) depends on its position
5  6  7  .  9  1  4
MSD      Decimal     LSD
point
Positional values      2    1    0        -1    -2    -3
(weights)               10 10 10     10  10 10
We will write ( 5 6 7. 9 1 4)
10
Binary:
Base-2 Number System
1   0   1   1   1   1  .   0   0   1
2   2    2    2    2    2       2    2    2
5   4   3    2    1    0       -1   -2   -3
We write:  ( 1 0 1 1 1 1 . 0 0 1 )
2
base point or radix
Digits are called bits
Binary Representation
• The basis of all digital data is binary representation.
• Binary  -  means ‘two’
– 1, 0
– True, False
– Hot, Cold
– On, Off
• We must be able to handle more than just values for
real world problems
– 1, 0,  56
– True, False, Maybe
– Hot, Cold, LukeWarm, Cool
– On, Off, Leaky
Page 5

Number Systems
• Stone Age: knots, some stone marks
• Roman Empire: more systematic notation  I,
II, III, IV, V, VI, VII.VIII, IX, X, C=100,
D=500, M=1000, L=50
• Concept of zero by
– Maya- I century, Hindu-V century
• Positional-value systems: decimal, binary,
octal, etc..
Positional-Value System
• The value of a digit (“digit” from Latin word
for finger) depends on its position
5  6  7  .  9  1  4
MSD      Decimal     LSD
point
Positional values      2    1    0        -1    -2    -3
(weights)               10 10 10     10  10 10
We will write ( 5 6 7. 9 1 4)
10
Binary:
Base-2 Number System
1   0   1   1   1   1  .   0   0   1
2   2    2    2    2    2       2    2    2
5   4   3    2    1    0       -1   -2   -3
We write:  ( 1 0 1 1 1 1 . 0 0 1 )
2
base point or radix
Digits are called bits
Binary Representation
• The basis of all digital data is binary representation.
• Binary  -  means ‘two’
– 1, 0
– True, False
– Hot, Cold
– On, Off
• We must be able to handle more than just values for
real world problems
– 1, 0,  56
– True, False, Maybe
– Hot, Cold, LukeWarm, Cool
– On, Off, Leaky
Number Systems
• To talk about binary data, we must first talk about
number systems
• The decimal number system (base 10) you should
be familiar with!
– A digit in base 10 ranges from 0 to 9.
– A digit in base 2 ranges from 0 to 1 (binary number
system).  A digit in base 2 is also called a ‘bit’.
– A digit in base R can range from 0 to R-1
– A digit in Base 16 can range from 0 to 16-1
(0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F).  Use letters A-F to
represent values 10 to 15.  Base 16 is also called
Hexadecimal or just ‘Hex’.
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