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Graphing Calculator by Mathlab: User Manual
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  • Home
    • Introduction
    • PRO Features vs. FREE Version
    • Frequently Asked Questions, FAQs >
      • 1. How to Change the Number Format?
      • 2. How to Set Up the Separators Between Thousands?
      • 3. How to Set Precision?
      • 4. How to Send Feedback with Comments?
      • 5. How to import/export the library?
      • 6. How to Print Results?
      • 7. How to Make the Calculator Show the Results?
      • 8. How to Transport Calculation Results to other Programs?
      • 9. How to Transport Table to Other Platforms?
      • 10. How to Turn Off (or on) Vibration?
      • 11. How to Change the Language?
  • 1. Basics
    • 1.1. Navigation
    • 1.2. UI Elements
    • 1.3. Keyboard
    • 1.4. Input, Enter, Delete, Clear and UNDO Buttons
    • 1.5. Workspace Area
    • 1.6. Editing the Expression/Equation
    • 1.7. Using the Last Answer
    • 1.8. Writing Comments
    • 1.9. Clear, Copy & Paste Commands
    • 1.10. Rearranging Rows
  • 2. Settings
    • 2.1. General
    • 2.2. Calculator
    • 2.3. Graph
  • 3. Library
    • 3.1. Constants
    • 3.2. Functions
    • 3.3. How to Save Calculation Result/Graph to Library?
  • 4. Graph Mode
    • 4.1. 2D Graphing
    • 4.2. 3D Graphing
    • 4.3. Enlarging the Graph Area
    • 4.4. Changing to White Background
    • 4.5. Hide Keyboard
    • 4.6. Degree and Radian Scales
    • 4.7. Fixed Scale
    • 4.8. R-axis Scale
    • 4.9. Logarithmic Scale
    • 4.10. Tracing Values and Slopes
    • 4.11. Special Points: Roots and Criticals
    • 4.12. Intersections of Graphs
    • 4.13. Set Domain
    • 4.14. Show All - Roots, Critical Points and Intersections
    • 4.15. Fullscreen
  • 5. Table Mode
    • 5.1. Sharing of Functions
    • 5.2. 2D Table
    • 5.3. 3D Table
    • 5.4. Edit Functions
    • 5.5. Scroll Results
    • 5.6. Results Precision
    • 5.7. Zoom Controls
    • 5.8. Save and Load Table
    • 5.9. Table of Trigonometric Functions
  • 6. Numbers and Number Sense
    • 6.1. Decimals
    • 6.2. Fractions >
      • 6.2.1. Mixed Fractions
      • 6.2.2. Complex Fractions
      • 6.2.3. Converting Decimals to Fractions
      • 6.2.4. Converting Fractions to Decimals
    • 6.3. Percents
    • 6.4. Scientific Notation
    • 6.5. Engineering Notation
    • 6.6. Rounding Numbers
    • 6.7. Integer and Fractional Parts >
      • 6.7.1. Integer Part of a Number >
        • 6.7.1.1. Ceiling
        • 6.7.1.2. Floor
        • 6.7.1.3. Half Down
        • 6.7.1.4. Half to Even
        • 6.7.1.5. Half to Infinity
        • 6.7.1.6. Half to Odd
        • 6.7.1.7. Half to Zero
        • 6.7.1.8. Half Up
        • 6.7.1.9. Truncate
      • 6.7.2. Greatest Integer is the Floor Function
      • 6.7.3. Least Integer is the Ceiling Function
      • 6.7.4. Fractional Part of a Number
    • 6.8. Order of Operations
    • 6.9. Least Common Multiple
    • 6.10. Greatest Common Divisor
    • 6.11. Modulo
    • 6.12. Binary, Octal, Decimal, Hexadecimal Numbers
    • 6.13. Complex Numbers
    • 6.14. The Polar Form of Complex Numbers
    • 6.15. Polar to Rectangular Coordinates
  • 7. Introductory Algebra
    • 7.1. Arithmetic Operations
    • 7.2. Exponents
    • 7.3. Absolute Values
    • 7.4. Variables
    • 7.5. Evaluating Expressions
    • 7.6. Polynomials
    • 7.7. Roots
    • 7.8. Logarithms
  • 8. Equations in One Variable
    • 8.1. Linear Equation
    • 8.2. Absolute Value Equation
    • 8.3. Quadratic Equation
    • 8.4. Cubic Equation
    • 8.5. Polynomial Equation
    • 8.6. Rational Equation
    • 8.7. Radical Equation
    • 8.8. Exponential Equation
    • 8.9. Logarithmic Equation
  • 9. Inequalities in One Variable
    • 9.1. Inequality Symbols
    • 9.2. Linear Inequalities
    • 9.3. Absolute Value Inequalities
    • 9.4. Quadratic Inequality
    • 9.5. Polynomial Inequalities
    • 9.6. Rational Inequalities
    • 9.7. Compound Inequalities
    • 9.8. Inequalities with Constants
  • 10. Equations and Inequalities in Two Variables
    • 10.1. Linear Equations
    • 10.2. Systems of Linear Equations
    • 10.3. Graphing Inequalities
    • 10.4. Multiple Graphing of Inequalities
    • 10.5. Graphing Systems of Inequalities
    • 10.6. Solving Implicit Equations
  • 11. Algebraic Functions and Graphs
    • 11.1. Plotting Points
    • 11.2. How to Graph Functions?
    • 11.3. Setting the Applied Domain
    • 11.4. Linear Function
    • 11.5. Absolute Value Function
    • 11.6. Quadratic Function
    • 11.7. Polynomial Functions
    • 11.8. Rational Functions
    • 11.9. Radical Functions
    • 11.10. Logarithmic Functions
    • 11.11. Exponential Functions
    • 11.12. Sign Function
    • 11.13. Multiple Graphing
    • 11.14. Piecewise Functions
  • 12. Matrices and Vectors
    • 12.1. Matrix Operations
    • 12.2. Editing Matrix Entries
    • 12.3. Matrix Variables
    • 12.4. Matrix and Vector Forms
    • 12.5. Variable Matrix to System of Linear Equations
    • 12.6. Solving Systems of Linear Equations Using Matrix Equations
  • 13. Trigonometric Functions and Their Inverses
    • 13.1. Degrees and Radians >
      • 13.1.1. Degrees, Minutes and Seconds
      • 13.1.2. Bradis Table
    • 13.2. Trigonometric Function Keys
    • 13.3. Trigonometric Values of Special Angles >
      • 13.3.1. The 45- 45 - 90 Triangle
      • 13.3.2. The 30-60-90 Triangle
      • 13.3.3. Quadrantal Angles
      • 13.3.4. Coterminal Angles
    • 13.4. Trigonometric Values of 15 Degrees and Its Multiples
    • 13.5. Hyperbolic Function Keys
    • 13.6. Graphing Trigonometric Functions
    • 13.7. Graphing Hyperbolic Functions
    • 13.8. Graphing Inverse Functions
  • 14. Analytic Geometry
    • 14.1. Conic Sections
    • 14.2. Parametric Equations
    • 14.3. Polar Graphs >
      • 14.3.1. Limacon
      • 14.3.2. Cardioid
      • 14.3.3. Lemniscate
      • 14.3.4. Rose
      • 14.3.5. Other Polar Graphs
    • 14.4. 3D Graphing
  • 15. Limits
    • 15.1. Right - hand Limit
    • 15.2. Left - hand Limit
    • 15.3. Limit of a Function
    • 15.4. Limit of a Polynomial Function
    • 15.5. Limit of a Rational Function
    • 15.6. Limit of a Radical Function
    • 15.7. Limit of an Absolute Value Function
    • 15.8. Limit of a Trigonometric Function
    • 15.9. Limit of an Exponential and Logarithmic Function
    • 15.10. Limit of a Piece-wise Function
    • 15.11. Limits at Infinity
    • 15.12. Indeterminate Forms
    • 15.13. Limit of a Hyperbolic Function
  • 16. Derivatives
    • 16.1. First Derivative Key
    • 16.2. Second Derivative Key
    • 16.3. Third and Higher Derivative Keys
    • 16.4. Rules of Differentiation
    • 16.5. Derivatives of Polynomial Functions
    • 16.6. Derivatives of Rational Functions
    • 16.7. Dervatives of Trigonometric, Logarithmic and and Exponential Functions
    • 16.8. More on Derivatives
  • 17. Partial Derivatives
    • 17.1. Increments
    • 17.2. Dervative of a Function df (or dy))
    • 17.3. Derivative of a Function df (f not in terms of x)
    • 17.4. Other Partial Derivatives
    • 17.5. Higher Order Partial Derivatives
    • 17.6. Total Derivates
  • 18. Definite Integral
    • 18.1. Definite Integral of Algebraic Functions
    • 18.2. Definite Integral of Trigonometric Functions
  • 19. Basic Statistics
    • 19.1. Summation Notation
    • 19.2. Product Notation
    • 19.3. Minimum and Maximum
    • 19.4. Factorial, nCr and nPr
    • 19.5. Measures of Central Tendency >
      • 19.5.1. Mean from Ungrouped Data Set
      • 19.5.2. Mean from Frequency Distribution Table
      • 19.5.3. Median from Ungrouped Data Set
      • 19.5.4. Mode
    • 19.6. Measures of Variability >
      • 19.6.1. Range
      • 19.6.2. Interquartile Range and Quartile Deviation
      • 19.6.3. Mean Absolute Deviation
      • 19.6.4. Variance and Standard Deviation
      • 19.6.5. Coefficient of Variation
    • 19.7. Measures of Position
    • 19.8. Bivariate Data Analysis >
      • 19.8.1 Covariance
      • 19.8.2. Correlation Coefficient
      • 19.8.3. Scatter Plot and Regression Line
  • 20. Special Functions
    • 20.1. Gamma Function
    • 20.2. Logarithmic Gamma Function
    • 20.3. Digamma Function
  • 21. List of ALL Functions
    • 21.1. Arithmetics
    • 21.2. Algebra
    • 21.3. Trigonometry
    • 21.4. Statistics
    • 21.5. Calculus

6.12. Binary, Octal, Decimal, Hexadecimal Numbers

Numbers can also be represented using the binary, octal and hexadecimal number systems.
Converting Decimal to Binary and Vice Versa

The binary system only uses the digits 0 and 1 to express a number. Each digit "1" in a binary code represents a power of 2 and each "0" represents a zero. For example, the binary code 1010111 means 1(2^6) + 0(2^5) + 1(2^4) + 0(2^3) + 1(2^2) + 1(2^1) + 1(2^0) = 64 + 0 + 16 + 0 + 4 + 2 + 1 = 87, so 1010111 in binary equals the decimal number 87.

In the app, type dec0b1010111 and see that the result is 87. The code “0b” is used to denote the number as a binary number. To convert 87 back to binary, type bin87. The calculator should display 0b1010111. The number following the “0b” code is the binary equivalent of 87.
Picture
Examples
Convert each decimal number to binary.
1) 105
2) 224
3) 100

Calculator Solutions
Type "bin" before each number.
1) bin(105)
2) bin(224)
3) bin(100)
Picture
Examples
Convert each binary number to a decimal number.
1) 1101001
2) 11100000
3) 1100100

Calculator Solutions
Type "dec" before each argument and denote the binary number by "0b."
1) dec(0b1101001)
2) dec(0b11100000)
3) dec(​0b1100100)
Picture
Converting Decimal to Octal and Vice Versa

The octal number system uses 8 digits (0, 1, 2, 3, 4, 5, 6, and 7) to represent a number. Because the digits only go up to 7, the system replaces the last digit for the number 8 and expresses it as 10, which means 1 × 8^1 + 0(8^0).

To see this conversion in the app, type oct8 and see that the display shows 0o10, meaning that the decimal number 8 is equivalent to 10 in the octal number system. The code “0o” means that the following number is an octal number.

To convert the octal number 10 back to a decimal number, type dec0o10. The result is 8.
Picture
Examples
Convert each decimal number to octal.
1) 105
2) 224
3) 100

Calculator Solutions
Type "oct" before each argument.
1) oct(105)
2) oct(224)
3) oct(100)
Picture
Examples
Convert each octal number to decimal.
1) 151
2) 340
3) 144

Calculator Solutions
Type "dec" before each argument and denote the octal number by "0o."
​1) dec(0o151)
2) dec(0o340)
​3) dec(0o144)
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Converting Decimal to Hexadecimal and Vice Versa

The hexadecimal number system is a base 16 numeral system. It uses 16 symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F) to represent a number. Unlike the octal and binary systems, it uses the first six letters of the alphabet (A, B, C, D, E and F). This means that after 9, the system counts to A for 10, B for 11, C for 12, D for 13, E for 14, and F for 15. Counting up from 15 replaces the last digit.

​For example, the decimal number 17 is expressed as 11 in the hexadecimal system. To see it in the app, type hex17 and the app will display 0x11. The first two symbols “0x” mean that the following number is a hexadecimal number. To convert the hexadecimal number 11 back to decimal, type dec0x11 and the result will be 17.
Picture
Examples
Convert each decimal number to hexadecimal.
1) 105
2) 224
3) 100

Calculator Solutions
Type "hex" before each argument.
1) hex105
2) hex224
​3) hex100
Picture
Examples
Convert each hexadecimal number to decimal.
1) 69
2) E0
3) 64

Calculator Solutions
Type "dec" before each argument and denote the hexadecimal by "0x."
1) dec(0x69)
2) dec(0xE0)
​3) dec(0x64)
Picture
Converting Between Number Systems
Remember to enter the code “0b” to convert a binary number, “0o” to convert an octal number, and “0x” to convert a hexadecimal number.

Examples
1) Convert 10011001 to hexadecimal.
2) Convert 1234E to binary.
3) Convert A045 to octal.
4) Convert 012576 to binary.
5) Convert 101011 to octal.

Calculator Solutions
1) Type: hex(0b10011001)
   The binary 10011001 is equivalent to 99 in hexadecimal.

2) Type: bin(0x1234E)
    The hexadecimal 1234E is equivalent to 10010001101001110.

3) Type: oct0xA045
     The hexadecimal A045 is equivalent to 120105 in octal.

4) Type: bin0o012576
    The octal 012576 is equivalent to 1010101111110 in binary.

5) Type: oct0b101011
    The binary 101011 is equivalent to 53 in octal.
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