Page 1 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’.Read More

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