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- 1. Number System T- 1-855-694-8886 Email- info@iTutor.com By iTutor.com
- 2. Number system In earlier days, people used to exchange their things for other things. The requirement for numbers primarily originated from the need to count. They used the numbers 1,2,3,.that served the people for many years because all they needed to count was their crops, and animals. Later on numbers such as zero, integers, rational numbers, irrational numbers were introduced. There is evidence that as early as 30,000 BC our ancient ancestors were tallying or counting things. That is where the concept of number systems began. © iTutor. 2000-2013. All Rights Reserved
- 3. Numbers Natural Numbers: A natural number is a number that comes naturally, Natural numbers are greater than zero we can use this numbers as counting numbers: {1, 2, 3, 4, 5, 6 ….…, }. Whole numbers: Whole numbers are just all the natural numbers plus a zero: {0, 1, 2, 3, 4, 5, ……………… , }. If our system of numbers was limited to the Natural Numbers then a number such as –2 would have no meaning. The next number system is the Integers. © iTutor. 2000-2013. All Rights Reserved
- 4. numbers Integers: Integers include the Natural numbers, zero, and the negative Natural numbers. Numbers in the form of negative and positive numbers { ….-4, -3, -2, -1, 0, 1, 2, 3,4, …. }. Rational number: Which can be written in the form of . Where p and q are integers and q ≠ 0 is called a rational number, so all the integers are rational number . q p © iTutor. 2000-2013. All Rights Reserved
- 5. numbers Irrational numbers : The number can not be written in the form of . Pythagorean in Greece were first to discover irrational number . 2, 3, are irrational number . q p © iTutor. 2000-2013. All Rights Reserved
- 6. numbers Real numbers: All the numbers including rational and irrational numbers are called real number The official symbol for real numbers is a bold R. Prime numbers: The real number which is divisible by 1 and itself is called prime number Ex- 1,2,3,5,7,11,13,17, ….. © iTutor. 2000-2013. All Rights Reserved
- 7. The Real Number System Real Numbers (all numbers are real) Rational Numbers Irrational Numbers …-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 Integers Whole Numbers Natural Numbers …any number that is not rational Example: = 3.14159…… e= 2.71828….. Which can be written in the form of . q p © iTutor. 2000-2013. All Rights Reserved
- 8. Number system A number system defines how a number can be represented using distinct symbols. A number can be represented differently in different systems. For example, the two numbers (2A)16 and (52)8 both refer to the same quantity, (42)10, but their representations are different. © iTutor. 2000-2013. All Rights Reserved
- 9. Common Number Systems Number system can be categorized as Decimal number system Binary number system Octal number system Hexadecimal Number System © iTutor. 2000-2013. All Rights Reserved
- 10. Common Number Systems Each number system is associated with a base or radix The decimal number system is said to be of base or radix 10 A number in base r contains r digits 0,1,2,...,r-1 Decimal (Base 10): 0,1,2,3,4,5,6,7,8,9 © iTutor. 2000-2013. All Rights Reserved 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 Hexa- decimal 16 0, 1, … 9, A, B, … F No No
- 11. 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}. © iTutor. 2000-2013. All Rights Reserved 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.
- 12. 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 is S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F} 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. © iTutor. 2000-2013. All Rights Reserved
- 13. The octal system (base 8) The word octal is derived from the Latin root octo (eight). In this system the base b = 8 and we use eight symbols to represent a number. The set of symbols is: S = {0, 1, 2, 3, 4, 5, 6, 7} © iTutor. 2000-2013. All Rights Reserved
- 14. 14 Converting Decimal to Binary To convert a decimal integer into binary, keep dividing by 2 until the quotient is 0. Collect the remainders in reverse order To convert a fraction, keep multiplying the fractional part by 2 until it becomes 0. Collect the integer parts in forward order Example: 162.375: So, (162.375)10 = (10100010.011)2 162 / 2 = 81 rem 0 81 / 2 = 40 rem 1 40 / 2 = 20 rem 0 20 / 2 = 10 rem 0 10 / 2 = 5 rem 0 5 / 2 = 2 rem 1 2 / 2 = 1 rem 0 1 / 2 = 0 rem 1 0.375 x 2 = 0.750 0.750 x 2 = 1.500 0.500 x 2 = 1.000 © iTutor. 2000-2013. All Rights Reserved
- 15. 15 Octal and Hexadecimal Numbers The octal number system: Base-8 Eight digits: 0,1,2,3,4,5,6,7 The hexadecimal number system: Base-16 Sixteen digits: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F For our purposes, base-8 and base-16 are most useful as a “shorthand” notation for binary numbers 10 1012 8 )5.87(84878281)4.127( 10 0123 16 )46687(16151651661611)65( FB © iTutor. 2000-2013. All Rights Reserved
- 16. The end For more information call us 1-855-694-8886 Visit www.iTutor.com

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