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Topic 1 Number Systems Single Slide

# Topic 1 Number Systems Single Slide - Topic 1 Number...

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Topic 1 Number Systems Akash Kumar

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Outline Analog and Digital systems Positional number systems Binary, octal, decimal, hexadecimal Conversions between number systems Basic binary addition, subtraction and multiplication Signed binary number representations Signed magnitude, One’s complement, Two’s complement Signed binary addition and subtraction Binary coded decimal (BCD) representation 2
Analog Systems Analog Systems V(t) can have any value between its minimum and maximum value V(t) t 3

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Digital Systems Digital Systems V(t) must take a value selected from a set of values called an alphabet Binary digital systems form the basis of almost all hardware systems currently V(t) For example, Binary Alphabet: 0, 1. 10 1 0 1 t 4
Slide example Consider a child’s slide in a playground: continuous movement a set of discrete steps levels 5

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Exercise Explain whether the following are analog or digital: A painting Facebook profile picture Sounds when you talk to your neighbor Tweet to your neighbor 6
NUMBER SYSTEMS 7

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Four Important Number Systems System Why? Remarks Decimal 10 fingers Binary ON/OFF systems 3 times more digits than decimal Octal Shorthand notation for working with binary 3 times less digits than binary Hex ------- do --------- 4 times less digits than binary 8
Positional Number Systems Have a radix r (base) associated with them. In the decimal system, r = 10, and there are 10 symbols, 0 - 9. What does 642.391 10 mean?? 6 x 10 2 + 4 x 10 1 + 2 x 10 0 . 3 x 10 -1 + 9 x 10 -2 + 1 x 10 -3 Radix point Increasingly +ve powers of radix Increasingly -ve powers of radix 9

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Positional Number Systems 100 (10 2 ) 10 (10 1 )1 ( 1 0 0 ) 0.1 (10 -1 ) 0.01 (10 -2 ) 0.001 (10 -3 ) 64 2 39 1 600 40 2 0.3 0.09 0.001 = 600 + 40 + 2 + 0.3 + 0.09 + 0.001 = 642.391 What does 642.391 10 mean?? Radix point Multiply each digit by appropriate power of 10 and add them together 10
Positional Number Systems Number system Radix Symbols Binary 2 {0,1} Octal 8 {0,1,2,3,4,5,6,7} Decimal 10 {0,1,2,3,4,5,6,7,8,9} Hexadecimal 16 {0,1,2,3,4,5,6,7,8,9,a,b,c,d,e,f} 11

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Positional Number Systems Decimal Octal Decimal Octal 00 8 1 0 11 9 1 1 2 2 10 12 33 1 1 1 3 4 4 12 14 5 5 13 15 6 6 14 16 7 7 15 17 16 20 Octal Number System Note 14
Positional Number Systems Decimal Hex Binary Decimal Hex Binary 0 0 0 8 8 1000 1 1 1 9 9 1001 2 2 10 10 (Note) A 1010 3 3 11 B 1011 4 4 100 12 C 1100 5 5 101 13 D 1101 6 6 110 14 E 1110 7 7 111 15 F 1111 16 (Note) 10 10000 Hexadecimal Number System: 15

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CONVERSION BETWEEN NUMBER SYSTEMS 16
Conversion: Binary to Decimal 1 x 2 3 + 1 x 2 2 + 0 x 2 1 + 1 x 2 0 . 0 x 2 -1 + 1 x 2 -2 + 1 x 2 -3 = 13.375 10 Binary point Binary Decimal 1101.011 2 (??) 10 8 (2 3 )4 ( 2 2 )2 ( 2 1 )1 ( 2 0 ) 0.5 (2 -1 ) 0.25 (2 -2 ) 0.125 (2 -3 ) 11 01 1 84 0 0.25 0.125 = 8 + 4 + 1 + 0.25 + 0.125 = 13.375 17

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Conversion: Decimal to Binary 155 10 = 1 0011011 2
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Topic 1 Number Systems Single Slide - Topic 1 Number...

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