FLIPPED CLASS F#3- Number System. Department of CSE, Coimbatore CTPS 2018

Transcription

1 FLIPPED CLASS F#3- Number System Department of CSE, Coimbatore CTPS

2 Common Number Systems System Base Symbols Used by humans? Used in computers? Decimal 10 0, 1, 9 Yes No Binary 2 0, 1 No Yes Octal 8 0, 1, 7 No No Hexadecimal 16 0, 1, 9, A, B, F No No Department of CSE, Coimbatore 2

3 The decimal system (base 10) The word decimal is derived from the Latin root decem (ten). In this system the base b = 10 and we use ten symbols. S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} The symbols in this system are often referred to as decimal digits or just digits. Department of CSE, Coimbatore 3

4 Integers Integers are generally represented in the form as Eg. The place values for the integer number +24 is Department of CSE, Coimbatore 4

5 Real Numbers Real Numbers are generally represented in the form as Eg. The place values for the real number is Department of CSE, Coimbatore 5

6 The binary system (base 2) The word binary is derived from the Latin root bini(or two by two). In this system the base b = 2 and we use only two symbols. S = {0, 1} The symbols in this system are often referred to as binary digits or bits(binary digit). Department of CSE, Coimbatore 6

7 Decimal to Binary Conversion The number (156) 10 in decimal is the same as ( ) 2 in binary. Let us see how the conversion is done! Department of CSE, Coimbatore 7

8 Decimal to Binary Conversion Cntd.. If the decimal number to be converted is ( ) 10, let us see how the fractional part can be converted to binary! Department of CSE, Coimbatore 8

9 If the decimal number to be converted is ( ) 10, let us see how the fractional part can be converted to binary! The binary of (156) 10 is ( ) 2 and the binary of (0.6875) 10 is (0.1011) 2 So the complete answer is ( ) 10 = ( ) 2 Department of CSE, Coimbatore 9

10 The number (11001) 2 in binary is the same as 25 in decimal and is represented as The equivalent decimal number is N = = 25. Department of CSE, Coimbatore 10

11 The number (101.11) 2 in binary is equal to the number 5.75 in decimal. Department of CSE, Coimbatore 11

12 Can you perform the indicated conversion? Decimal to Binary Binary to Decimal a) =? b) =? c) =? d) =? a) =? b) =? c) =? d) =? Department of CSE, Coimbatore 12

13 Decimal Binary..Answers a) =? b) =? c) =? d) =? Department of CSE, Coimbatore 13

14 Binary Decimal.Answers a) =? b) =? c) =? d) =? Department of CSE, Coimbatore 14

15 The hexadecimal system (base 16) The word hexadecimal is derived from the Greek root hex (six) and the Latin root decem (ten). In this system the base b = 16 and we use sixteen symbols to represent a number. The set of symbols are: S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,A, B, C, D, E, F} Note that the symbols A, B, C, D, E, F are equivalent to 10, 11, 12, 13, 14, and 15 respectively. The symbols in this system are often referred to as hexadecimal digits. Department of CSE, Coimbatore 15

16 The number (2AE) 16 in hexadecimal is equivalent to 686 in decimal is represented as The equivalent decimal number is N = = 686. Department of CSE, Coimbatore 16

17 Converting from base 10 to base = Department of CSE, Coimbatore 17

18 Decimal to any base Integral part Department of CSE, Coimbatore 18

19 Decimal to any base Fractional part Department of CSE, Coimbatore 19

20 Binary-octal (base 8) conversion The binary bits are grouped into 3 and converted. Binary to octal and octal to binary conversion. Eg. Department of CSE, Coimbatore 20

21 Binary-hexadecimal conversion The binary bits are grouped into 4 and converted Binary to hexadecimal and hexadecimal to binary conversion. Eg. Department of CSE, Coimbatore 21

22 Octal (base 8)-hexadecimal conversion Convert into binary first and then perform the required conversion. Octal to hexadecimal and hexadecimal to octal conversion. Eg. Department of CSE, Coimbatore 22

23 Try it yourself Convert these binary numbers into octal numbers... (a) (8 bits) (b) (8 bits) Convert the following octal numbers into hexadecimal (16 bits) (a) 65 8 (b) Can you find out... What is the biggest binary number one can write with n bits? How many unique patterns does a sequence of 5 bits generate? Write all the patterns of a sequence of 5 bits. Department of CSE, Coimbatore 23

24 Try it yourself Convert these binary numbers into octal numbers... (a) (8 bits) (b) (8 bits) Convert the following octal numbers into hexadecimal (16 bits) (a) 65 8 (b) Can you find out... What is the biggest binary number one can write with n bits? How many unique patterns does a sequence of 5 bits generate? Write all the patterns of a sequence of 5 bits. Department of CSE, Coimbatore 24

25 Binary Octal... Answers Refer to the binary-octal conversion table = 57 8 Refer to the binary-octal conversion table = Department of CSE, Coimbatore 25

26 Octal Hexadecimal Answers Refer to the binary-octal conversion table = Refer to the binary-octal conversion table = Department of CSE, Coimbatore 26

27 Conversion from Hexadecimal to Binary Replace each hex digit by the 4 equivalent bits, for examples, A3C5H = B 102AH = B Department of CSE, Coimbatore 27

28 Conversion from Binary to Hexadecimal Starting from the right-most bit (least-significant bit), replace each group of 4 bits by the equivalent hex digit (pad the left-most bits with zero if necessary), for example, B = B = 24AH B = B = 22CBH Department of CSE, Coimbatore 28

29 Exercises (Number Systems Conversion) Convert the following decimal numbers into binary and hexadecimal numbers:

30 Answers 108 = = 6C 4848 = = 12F = = 2328 Depart ment of 30 CSE, Coimb atore

31 Exercises (Number Systems Conversion) Convert the following binary numbers into hexadecimal and decimal numbers:

32 Answers = 218H = 536D = 80H = 128D = AAAH = 2730D Depart ment of 32 CSE, Coimb atore

33 Exercises (Number Systems Conversion) Convert the following hexadecimal numbers into binary and decimal numbers: ABCDE F 33

34 Answers ABCDE = = D 1234 = = 4660D 80F = = 2063D 34

35 Exercises (Number Systems Conversion) Convert the following decimal numbers into binary equivalent: 19.25D D 35

36 Answers = = Depart ment of 36 CSE, Coimb atore