Number Systems Basic Concepts

Number Systems Basic Concepts

• 1.
  NUMBER SYSTEMSFOR-IAN V. SANDOVAL
• 2.
  • Analyze thenumber systems handled by digital computing devices to process data • Convert decimal to binary • Solve Binary Arithmetic • Extend understanding of other number systems (Octal and Hexadecimal) Learning Objectives
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  • Decimal NumberSystem • Data Representation in Digital Computing • Binary Number System Contents
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  NUMBER SYSTEMS • digitaldevices deals with numbers • decimal number system for numerical calculations • number system used to represents numerical data when using the computer
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  DECIMAL NUMBER SYSTEM •Base 10 Number System • The word “Decimal” comes or derived from the Latin word “Ten” • The numerals run from 0 to 9 {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}; these numerals are called Arabic Numerals • Radix is the other term for the base of the number system
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  DECIMAL NUMBER SYSTEM •Power of 10 may be expressed as 100 or 1, 101 or 10, 102 or 100, etc. and this is called place value. • Each digit in decimal number system is called face value • Example: The digit 3 in the decimal integer 321 has a face value of 3 and place value of 102.
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  DECIMAL INTEGER • DecimalInteger is a string of decimal digits. • Example: 1234, 2509, etc.
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  DECIMAL FRACTION • DecimalFraction is a string of decimal digits with an embedded decimal point. • Example: 1234.56, 2509.325 etc. • In a decimal fraction, the place values to the right of the decimal are expressed to the negative powers of 10 such as 10-1 or 1/10 or 0.1, 10-2 or 1/100 or 0.01, etc.
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  EXPANDED NOTATION FORDECIMAL INTEGER • Any decimal integer can be expressed as the sum of each digit times the power of ten. For example, 2509 can be expressed as
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  EXPANDED NOTATION FORDECIMAL FRACTION • Any decimal fraction may also be expressed in expanded notation. For example, 2509.325 can be expressed as
• 11.
  DATA REPRESENTATION INDIGITAL COMPUTING • Data • Data Representation • Digitization • Digital Revolution
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  DATA REPRESENTATION INDIGITAL COMPUTING
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  DATA REPRESENTATION INDIGITAL COMPUTING Representing Decimal Data by Binary Components
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  DATA REPRESENTATION INDIGITAL COMPUTING
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  DATA REPRESENTATION INDIGITAL COMPUTING
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  REPRESENTING NUMBERS
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  REPRESENTING TEXT
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  REPRESENTING TEXT
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  REPRESENTING TEXT
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  REPRESENTING TEXT –ASCII TABLE
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  REPRESENTING TEXT –EXTENDED ASCII CODES
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  REPRESENTING TEXT
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  BINARY NUMBER SYSTEM •Binary is derived from the Latin word for “Two” • Two or 2 is the base for the binary number system • It uses only two numerals (0 & 1); these are called as BITS. A bit is a short term for binary digits. • Zero or 0 represents the absence of an assigned value • One or 1 represents the presence of the assigned value
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  BINARY NUMBER SYSTEM
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  BINARY INTEGERS • binarynumbers that do not have fractional part or without an embedded binary point. • Example: 1012 , 11102 , etc.
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  BINARY FRACTIONS • binarynumbers with an embedded binary point • Example: 110.012 , 10110.0102 , etc.
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  DECIMAL TO BINARYCONVERSIONS • Convert 6310 number system to binary number system.
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  DECIMAL TO BINARYCONVERSIONS • Convert 6310 number system to binary number system.
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  BINARY TO DECIMALCONVERSIONS OF INTEGERS • Convert 10012 to decimal number system
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  SEAT WORK ACTIVITY
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  DECIMAL TO BINARYCONVERSIONS OF FRACTIONS • Convert the decimal fraction 0.37510 to binary fraction.
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  DECIMAL TO BINARYCONVERSIONS OF FRACTIONS • Convert the decimal fraction 0.37510 to binary fraction.
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  NON-TERMINATION CONVERSIONS OFFRACTIONS • The decimal fraction 0.810 is to be converted to its binary equivalent.
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  DECIMAL TO BINARY CONVERSIONSWITH INTEGRAL & FRACTIONAL PARTS • Convert the decimal number 24.62510 to its binary equivalent.
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  DECIMAL TO BINARY CONVERSIONSWITH INTEGRAL & FRACTIONAL PARTS • Convert the decimal number 24.62510 to its binary equivalent.
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  DECIMAL TO BINARY CONVERSIONSWITH INTEGRAL & FRACTIONAL PARTS • Convert the decimal number 24.62510 to its binary equivalent.
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  BINARY TO DECIMAL CONVERSIONSWITH INTEGRAL & FRACTIONAL PARTS • Convert the binary number 11.0112 to its decimal equivalent.
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  SEAT WORK ACTIVITY
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  BINARY ADDITION • Fourpossible combinations when adding these two binary numbers: 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 0 plus a carry-over of 1
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  BINARY ADDITION C
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  BINARY ADDITION C C
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  BINARY SUBTRACTION • Thetable for binary subtraction is as follows: 0 – 0 = 0 1 – 1 = 0 1 – 0 = 1 0 – 1 = 0 with a barrow of 1
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  BINARY SUBTRACTION
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  BINARY SUBTRACTION
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  BINARY SUBTRACTION
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  BINARY MULTIPLICATION • Thetable for binary multiplication is as follows: 0 x 0 = 0 0 x 1 = 0 1 x 0 = 0 1 x 1 = 1
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  BINARY MULTIPLICATION
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  BINARY DIVISION • Thetable for binary division is as follows: 0 / 0 = 0 0 / 1 = 0 1 / 1 = 1 1 / 0 = cannot be
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  BINARY DIVISION
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  BINARY DIVISION
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  BINARY DIVISION
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  SEAT WORK ACTIVITY
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  BINARY DIVISION • Thetable for binary division is as follows: 0 / 0 = 0 0 / 1 = 0 1 / 1 = 1 1 / 0 = cannot be
• 54.
  OCTAL NUMBER SYSTEM •Octal is derived from the Greek word meaning “eight”. • The octal number system was adapted because of the difficulty of dealing with long strings of binary 0s and 1s in converting them into decimals. • The radix for the number system is 8. • It uses 8 basic digits {0, 1, 2, 3, 4, 5, 6, and 7}.
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  OCTAL NUMBER SYSTEM Powerof Eight and its equivalent decimal value
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  OCTAL NUMBER SYSTEM OctalNumber and its equivalent Decimal number
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  DECIMAL TO OCTALCONVERSION • Convert the decimal number 1910 to its equivalent octal number.
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  OCTAL TO DECIMALCONVERSION • Convert the octal number 4858 to its equivalent decimal number.
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  OCTAL TO BINARYCONVERSION • Convert the octal number 7328 to its equivalent binary number.
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  BINARY TO OCTALCONVERSION • Convert the binary number 101101112 to its equivalent octal number.
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  SEAT WORK ACTIVITY
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  HEXADECIMAL NUMBER SYSTEM •The term “hexadecimal” is derived from the combining Greek word “six” with the Latin word “ten”. • It uses 10 numerals {0,1,2,3,4,5,6,7,8 & 9} and letter {A, B, C, D, E & F}. • The radix of the number system is 16.
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  HEXADECIMAL NUMBER SYSTEM HexadecimalNumber and its equivalent Decimal number
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  HEXADECIMAL NUMBER SYSTEM Powerof sixteen and its equivalent decimal value
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  DECIMAL TO HEXADECIMALCONVERSION • Convert the decimal number 5910 to its equivalent hexadecimal number.
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  HEXADECIMAL TO DECIMALCONVERSION • Convert the hexadecimal number AD16 to its equivalent decimal number.
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  HEXADECIMAL TO BINARYCONVERSION • Convert the hexadecimal number 1AC16 to its equivalent binary number.
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  BINARY TO HEXADECIMALCONVERSION • Convert the binary number 100111012 to its equivalent hexadecimal number.
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  SEAT WORK ACTIVITY
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  REFERENCES Byte-Notes (n.d.). NumberSystem in Computer. Retrieved from https://byte-notes.com/number-system- computer/. Cook, D. (n.d.). Number Systems. Retrieved from https://www.robotroom.com/NumberSystems.html. GeeksforGeeks (n.d.). Number System and Base Conversion. Retrieved from https://www.geeksforgeeks.org/number-system-and-base-conversions/. Mendelson, E. (2008). Number Systems and the Foundation of Analysis. New York: Dover Publications, Inc. TutorialPoints (n.d.). Number System Conversion. Retrieved from https://www.tutorialspoint.com/computer_logical_organization/number_system_conversion.htm