The NBP Calculator Version: 1.15.161 Date: 2019-09-30 23:43 UTC Organization: National Braille Press Contact: Brian Mac Donald Address: 88 St. Stephen Street Boston, MA 02115 United States of America 1 Overview This calculator has been designed to be as usable as possible not only by sighted people but also by blind people using speech and/or a braille device. It's easy to use via it's own on-screen calculator-style keys, a full on-screen keyboard, or an externally-connected Bluetooth or USB keyboard. It offers the following features: * Real and complex decimal operations. * Fixed, scientific, and engineering notation. * Trigonometric functions that support radians, degrees, and gradians. * Unit conversion. * Integer and bitwise hexadecimal operations. * Predefined variables for common scientific constants. * Management of persistent user-defined variables. 1.1 Screen Layout This subsection contains screen layout images that've been intentionally drawn using traditional ASCII art. This has been done so that a blind person can easily "look" at them because screen readers are notoriously poor at dealing with graphical images. In both portrait and landscape modes, the result line is immediately above the expression line and the Clear button is immediately below it at the very left. This is to make expression entry as easy as possible for a blind person using a braille device. Moving backward one position enables him/her to quickly check the result, and moving forward one position allows him/her to easily clear the expression. Layout Legend CAPTION: Layout Legend AltKp Alternate Keypad selector AUSel Angle Unit selector BkSpc Backspace button Clear Clear button CMSel Calculator Mode selector Del Delete button DNSel Decimal Notation selector Down Down button Erase Erase button f(x) f(x) button Left Left button Right Right button Store Store button Up Up button Var Variable button 1.1.1 Portrait The screen has the following layout when in portrait mode: +---------------------------------------+ | The Result Output Area | +---------------------------------------+ | The Expression Input Area | +-------+-------+-------+-------+-------+ | Clear | AltKp | CMSel | DNSel | AUSel | +-------+-------+-------+-------+-------+ | Var | Store | BkSpc | Up | Del | +-------+-------+-------+-------+-------+ | f(x) | Erase | Left | Down | Right | +-------+-------+-------+-------+-------+ | | | | | The Currently Selected Keypad | | | | | +---------------------------------------+ 1.1.2 Landscape The screen has the following layout when in landscape mode: +-------------------------------------------------------+ | The Result Output Area | +-------------------------------------------------------+ | The Expression Input Area | +-------+-------+-------+-------------------------------+ | Clear | AltKp | CMSel | | +-------+-------+-------+ | | DNSel | Var | Store | | +-------+-------+-------+ | | AUSel | f(x) | Erase | The Currently Selected Keypad | +-------+-------+-------+ | | BkSpc | Up | Del | | +-------+-------+-------+ | | Left | Down | Right | | +-------+-------+-------+-------------------------------+ 1.2 Result Line This output area displays the on-going current result of evaluating what's been entered in the expression line. If no data has been entered yet then 0 is displayed. If the expression can't be evaluated at the moment (e.g. due to missing data or syntax errors) then the last known result, preceded by a question mark [?], is displayed. The displayed value begins with zero or more open brackets [(] - one for each bracket nesting level that hasn't yet been closed. Expression evaluation only considers the current bracket nesting level. To illustrate, here's what's displayed as the expression (2+3)×(4−(5+6)×7) is entered: Expression Result 0 ( (? (2 (2 (2+ (?2 (2+3 (5 (2+3) 5 (2+3)× ?5 (2+3)×( (?5 (2+3)×(4 (4 (2+3)×(4− (?4 (2+3)×(4−( ((?4 (2+3)×(4−(5 ((5 (2+3)×(4−(5+ ((?5 (2+3)×(4−(5+6 ((11 (2+3)×(4−(5+6) (−7 (2+3)×(4−(5+6)× (?−7 (2+3)×(4−(5+6)×7 (−73 (2+3)×(4−(5+6)×7) −365 1.3 Expression Line This input area is where the expression to be evaluated is entered (see Expressions for syntax). It's current content is persistent. The expression can be entered by pressing the calculator-style keys on the screen, via a full on-screen keyboard (tap this line to open it), or via an external keyboard. Additionally, the navigation buttons can be used to edit the expression. The result of evaluating the expression is displayed on the result line. It's kept up-to-date as the expression is being entered and/or edited. 1.3.1 Enter Key Typing this key completes the expression. The expression is added to the expression history, the expression line is cleared, and the final result is displayed on the result line. If there's an error then the cursor is placed at the error's location and the message is displayed on the result line. Pressing the = key on any of the keypads performs this same action. 1.3.2 Shortcuts the following actions can be performed by typing shortcuts on a keyboard: CAPTION: Expression Shortcuts Character Action CTRL-A Long press the Angle Unit selector. CTRL-C Press the Clear button. CTRL-D Press the Down button. CTRL-E Press the Erase button. CTRL-F Press the f(x) button. CTRL-K Set the input focus to the Keypad. CTRL-M Long press the Calculator Mode selector. CTRL-N Long press the Decimal Notation selector. CTRL-S Press the Store button. CTRL-U Press the Up button. CTRL-V Press the Variable button. 1.3.3 Expression History A history of successfully completed expressions is maintained. An expression is considered complete if there are no syntax errors within it when either the = key on any of the keypads is pressed or when the Enter key is typed. * Pressing the Up key moves backward through the history. * Pressing the Down key moves forward through the history. * Long pressing the Up key moves to the earliest entry in the history. * Long pressing the Down key moves to the most recent entry in the history. Any history entry can be edited and recompleted, although the history entries themselves are never actually changed. Edits to an entry are lost when moving away (up or down) from it without recompleting it. Recompleting a history entry adds it as a new entry. 1.4 Control Buttons 1.4.1 Clear Pressing this button clears the expression line. 1.4.2 Alternate Keypad Repeatedly pressing this button cycles through all of the keypads associated with the current calculator mode. A long press switches to the mode's primary keypad. This button is disabled if the mode only has one keypad. 1.4.3 Calculator Mode Repeatedly pressing this button cycles through all of the calculator modes. A long press presents a list from which the desired mode can be selected. The button's label is a three-letter abbreviation for the current selection. The current selection is persistent. The following modes are available: DEC Decimal (the default). This mode performs real and complex operations on IEEE 64-bit floating-point (commonly known as double) values. They consist of a 1-bit sign, an 11-bit exponent, and a 52-bit significand. Other than 0 (which is a special case), the smallest absolute value that this representation supports is 2^-1074 or approximately 5×10^−324, and the largest absolute value that it supports is 2^1023 or approximately 1.8×10^308. Calculations are performed with an accuracy of 15 significant digits. This mode supports complex numbers. The imaginary component, if nonzero, is displayed as either an addition to or a subtraction from the real component. If a number doesn't have an imaginary component then only its real component is displayed. If it does have an imaginary component but doesn't have a real component then only the imaginary component is displayed. Here are some examples: + 0 + 1 + i + 2i + −3 + −4i + 5 + i + −6 + 2i + −7 − 3i + 2.3×10^4 + 5.6×10^7i The keypads associated wit this mode are: + Decimal + Function + Conversion HEX Hexadecimal. This mode performs unsigned integer and bitwise operations on 64-bit values. Both input and output are in base 16 and use hexadecimal digits. Digits A through F are always displayed in uppercase but may be input in either case. A number may consist of up to 16 hexadecimal digits. The keypads associated wit this mode are: + Hexadecimal 1.4.4 Decimal Notation Repeatedly pressing this button cycles through all of the decimal notations. A long press presents a list from which the desired notation can be selected. The button's label is a three-letter abbreviation for the current selection. The current selection is persistent. The following notations are available: FXD Fixed (the default). If the absolute value of the number is less than 10^12 [1,000,000,000,000] and greater than or equal to 10^-3 [0.001] then it's displayed with its decimal point in its natural position. Its power of ten multiplier (e.g. ×10^x) isn't displayed (because it's 0), and digit grouping separators (e.g. 1,000) are displayed (to ease readability). If the number is an integer then the decimal point isn't displayed. If the number is outside this range then it's considered to be too difficult to intuitively read in fixed notation, and scientific notation is used instead. SCI Scientific. The number is always displayed such that its absolute value is greater than or equal to 1 and less than 10. In other words, there's always exactly one digit before the decimal point. If the rest of the digits (other than the first one) are 0 then the decimal point isn't displayed. If it needs to be multiplied by a power of 10 (either positive or negative) then ×10^x is appended. ENG Engineering. This is identical to scientific notation except that the power of ten is always a multiple of 3 and up to 3 digits are displayed before the decimal point. In all cases, the sign is only displayed if the number is negative. This is also true for the power of ten. CAPTION: Comparison of Decimal Notations Fixed 0.0123 456,789 Scientific 1.23×10^-2 4.56789×10^5 Engineering 12.3×10^-3 456.789×10^3 1.4.5 Angle Unit Repeatedly pressing this button cycles through all of the trigonometric angle units. A long press presents a list from which the desired unit can be selected. The button's label is a three-letter abbreviation for the current selection. The current selection is persistent. The following units are available: DEG Degrees (the default). A circle is divided into 360 degrees. RAD Radians. A circle is divided into 2π radians. GON Gradians (also known as grads or gons). A circle is divided into 400 gradians. 1.5 Memory Buttons These keys provide easy access to the predefined variables and to the predefined functions. They can also be used to manage user-defined variables. CAPTION: The Memory Keypad Var Store f(x) Erase 1.5.1 Variable Pressing this button presents a list of the user-defined variables followed by the predefined variables. Each line contains the name and current value of a variable. For a predefined variable, it also contains its description. Selecting a variable from this list enters its name into the expression line. The following actions are also available: Cancel Dismiss the list without taking any action. 1.5.2 Store Pressing this button presents a list of the user-defined variables. Each line contains the name and current value of a variable. Selecting a variable from this list assigns the value currently shown on the result line to it. The following actions are also available: Cancel Dismiss the dialog without taking any action. New Present a dialog for entering the name of a new variable. This dialog doesn't allow an existing variable to be overwritten. It offers the following actions: Cancel Dismiss the dialog without taking any action. Store Assign the value currently shown on the result line to to the new variable. This action is disabled when the name field is empty and when it contains the name of an existing variable. Variables can also be created or updated via the = operator within an expression. For example: * x = 1 * x = y = 2 * x = 3 + y = 4 + z = 5 To clarify: the last example sets z to 5, y to 9, and x to 12. 1.5.3 Erase Pressing this button presents a list of the user-defined variables. Each line contains the name and current value of a variable. Selecting a variable from this list removes its definition. The following actions are also available: Cancel Dismiss the dialog without taking any action. A long press presents the same list in a way that allows several variable definitions to be removed at once. It offers the following additional actions: Erase Remove the definitions of all the variables that have been selected. 1.5.4 f(x) Pressing this button presents a list of the predefined functions. Each line contains the name and description of a function. Selecting a function from this list enters its name, followed by an open bracket, into the expression line. The following actions are also available: Cancel Dismiss the dialog without taking any action. 1.6 Navigation Buttons These keys are particularly useful to blind people who are using a touch screen and a speech-based screen reader. CAPTION: The Navigation Keypad Backspace Up Delete Left Down Right 1.6.1 Left Pressing this button moves the cursor one character to the left. A long press moves the cursor all the way to the left. This button is disabled when the cursor is to the left of the first character. 1.6.2 Right Pressing this button moves the cursor one character to the right. A long press moves the cursor all the way to the right. This button is disabled when the cursor is to the right of the last character. 1.6.3 Backspace Pressing this button deletes the character immediately to the left of the cursor. A long press deletes all of the characters to the left of the cursor. This button is disabled when the cursor is to the left of the first character. 1.6.4 Delete Pressing this button deletes the character immediately to the right of the cursor. A long press deletes all of the characters to the right of the cursor. This button is disabled when the cursor is to the right of the last character. 1.6.5 Up Pressing this button moves to the previous entry in the expression history. A long press moves to the earliest (oldest) entry. This button is disabled when on the earliest entry. 1.6.6 Down Pressing this button moves to the next entry in the expression history. A long press moves to the latest (most recent) entry. This button is disabled when on the latest entry. 1.7 Keypads 1.7.1 Decimal This is the primary keypad for the Decimal calculator mode. It has the following layout: CAPTION: The Decimal Keypad ( ) " ' x⋅10^y 7 8 9 ÷ x^y 4 5 6 × ! 1 2 3 − % . 0 i + = Most of these keys enter whatever their label says into the expression line. The exceptions are: * The = key completes the expression. It's equivalent to typing the Enter key. * The x^y key enters ^ (the actual exponentiation operator). * The x⋅10^y key enters ×10^. It's for multiplying a number by a power of ten. The " and ' keys are for entering a number in the degrees"minutes'seconds format. Each of these components ("minutes and 'seconds) is optional. If specified, it's value must be an integer that's greater than or equal to 0 and less then 60. If omitted, it's value is assumed to be 0. If any of these components is specified then a decimal point may not be used. 1.7.2 Function This is the second keypad for the Decimal calculator mode. It has the following layout: CAPTION: The Function Keypad abs arg cnj rcp sin cos tan r2d asin acos atan d2r sinh cosh tanh sqrt exp log log10 cbrt e pi Each of these keys enters its function's name, followed by an open bracket [(], into the expression line. The exceptions are e and pi, which don't enter the open bracket because they're variables. 1.7.3 Conversion This is the third keypad for the Decimal calculator mode. It has the following layout: CAPTION: The Conversion Keypad Type From To DF2DC Type From To mi2km Type From To ac2ha Type From To cup2ml Type From To lb2kg Each four-key row is a separate key group. This allows five different unit conversions to be configured. Each of them, as shown above, defaults to a common US-to-International unit conversion. The first three keys configure the conversion: Type This key presents a list from which the desired unit type (e.g. length, area, volume) can be selected. From This key presents a list from which the unit that the supplied value is in can be selected. The list only contains units belonging to the currently configured type. To This key presents a list from which the unit that the supplied value is to be converted to can be selected. The list only contains units belonging to the currently configured type. The rightmost key is for actually performing the currently configured unit conversion. It's label shows what that conversion is in the form from2to (e.g. mi2km). This is the name of the predefined function that performs the conversion. Just like the keys on the Function keypad, pressing this key enters the name of this function, followed by an open bracket [(], into the expression line. Any of the unit conversion functions can be directly typed into the expression line. Because there are so many, none of them is included within the list presented by pressing the f(x) button. The most recently configured conversion for each unit type for each key group is persistent. 1.7.4 Hexadecimal This is the primary keypad for the Hexadecimal calculator mode. It has the following layout: CAPTION: The Hexadecimal Keypad ( ) < > % ^ C D E F ÷ | 8 9 A B × & 4 5 6 7 − ~ 0 1 2 3 + = Each of these keys enters whatever its label says into the expression line. The 0 through 9 and A through F keys are the 16 hexadecimal digits. The rest of the keys are as follows: Key Description = expression completion ( open bracket ) close bracket < logical left shift > logical right shift & bitwise and | bitwise inclusive or ^ bitwise exclusive or ~ bitwise ones complement + integer addition − integer subtraction or bitwise twos complement × integer multiplication ÷ integer division % integer remainder 2 Expressions 2.1 Elements 2.2 Operators 2.2.1 Infix 2.2.2 Prefix 2.2.3 Postfix 2.3 Using Variables 2.4 using Functions 2.4.1 Unit Conversion Functions 3 Reference 3.1 Variables 3.1.1 Predefined Variables CAPTION: Predefined Variables Name Value Description Units gamma 0.57721566490153286060 Euler-Mascheroni constant pi 3.14159265358979323846 ratio of circumference to diameter sigma 5.670367×10^−8 Stefan-Boltzmann constant W m^−2 K^−4 c 299,792,458 speed of light in vacuum m s^−1 e 2.71828182845904523536 base of natural logarithms h 6.626070040×10^−34 Planck constant J s i i imaginary unit k 1.38064852×10^−23 Boltzmann constant J K^−1 F 96,485.33289 Faraday constant C mol^−1 G 6.67408×10^−11 Newtonian constant of gravitation m^3 kg^−1 s^−2 L 6.022140857×10^23 Avogadro constant mol^−1 R 8.3144598 molar gas constant J mol^−1 K^−1 3.2 Functions 3.2.1 Predefined Functions CAPTION: Predefined Functinos Name Description abs(z) absolute value (modulus, magnitude) of complex number acos(x) trigonometric arc cosine acot(x) trigonometric arc cotangent acsc(x) trigonometric arc cosecant arg(z) arg (amplitude, phase) of complex number asec(x) trigonometric arc secant asin(x) trigonometric arc sine atan(x) trigonometric arc tangent cbrt(z) cube root of complex number ceil(x) round real number up to nearest integer cnj(z) conjugate of complex number cos(x) trigonometric cosine cosh(x) hyperbolic cosine cot(x) trigonometric cotangent coth(x) hyperbolic cotangent csc(x) trigonometric cosecant csch(x) hyperbolic cosecant d2r(x) convert real number from degrees to radians exp(z) natural exponential of complex number floor(x) round real number down to nearest integer gamma(z) gamma function of complex number imag(z) imaginary component of complex number log(z) natural log of complex number log10(z) log[10] of complex number neg(z) negation of complex number r2d(x) convert real number from radians to degrees rcp(z) reciprocal of complex number real(z) real component of complex number round(x) round real number to nearest integer sec(x) trigonometric secant sech(x) hyperbolic secant sin(x) trigonometric sine sinh(x) hyperbolic sine sqrt(z) square root of complex number tan(x) trigonometric tangent tanh(x) hyperbolic tangent 3.3 Unit Conversion 3.3.1 Angle CAPTION: Angle Units Symbol Name Calculation rad radians brad binary radians 1÷128 = 0.0078125 radians deg degrees pi÷180 = 0.0174533 radians rev revolutions 360 degrees crev centirevolutions 360÷100 = 3.6 degrees mrev millirevolutions 0.1 centirevolutions quad quadrants 360÷4 = 90 degrees sxt sextants 360÷6 = 60 degrees oct octants 360÷8 = 45 degrees sign signs 360÷12 = 30 degrees point points 360÷32 = 11.25 degrees hxct hexacontades 360÷60 = 6 degrees dmin arc minutes 1÷60 = 0.0166667 degrees dsec arc seconds 1÷60 = 0.0166667 arc minutes gon gradians 0.9 degrees gmin centesimal minutes 0.01 gradians gsec centesimal seconds 0.01 centesimal minutes 3.3.2 Area CAPTION: Area Units Symbol Name Calculation m2 SI meters^2 a ares 100 meters^2 ha hectares 100 ares sqin square inches 2.54^2 = 6.4516 centimeters^2 sqft square feet 12^2 = 144 square inches sqyd square yards 3^2 = 9 square feet sqrd square rods 5.5^2 = 30.25 square yards sqch square chains 4^2 = 16 square rods sqlink square links 0.01^2 = 10^−4 square chains sqfur square furlongs 10^2 = 100 square chains sqmi square miles 8^2 = 64 square furlongs sqlg square leagues 3^2 = 9 square miles ro roods 40 square rods ac acres 4 roods 3.3.3 Energy CAPTION: Energy Units Symbol Name Calculation J SI joules erg ergs 100 nanojoules Ry rydbergs 2.179872 attojoules eV electronvolts 160.217653 zeptojoules Ha hartrees 27.2107 electronvolts ftlbf foot pounds force 1.3558 joules BTU British thermal units 1055 joules thm therms 100,000 British thermal units hphr horsepower hours 2.6845 megajoules gasgal gasoline gallons 120 megajoules kWh kilowatt hours 3.6 megajoules cal small calories 4.184 joules Cal large calories 1,000 small calories 3.3.4 Force CAPTION: Force Units Symbol Name Calculation N SI newtons dyn dynes 10 micronewtons sn sthènes 1 kilonewton kgf kilograms force 9.80665 newtons lbf pounds force 4.4482216152605 newtons kip kips 1000 pounds force pdl poundals 0.138254954376 newtons 3.3.5 Length CAPTION: Length Units Symbol Name Calculation m SI meters in inches 2.54 centimeters ft feet 12 inches yd yards 3 feet rd rods 5.5 yards ch chains 4 rods link links 0.01 chains fur furlongs 10 chains mi miles 8 furlongs lg leagues 3 miles 3.3.6 Mass CAPTION: Mass Units Symbol Name Calculation g SI grams t tonnes 1 megagram Da daltons 1.660539040 yoctograms oz ounces 28.34952 grams dr drams 1÷16 ounces lb pounds 16 ounces stone stones 14 pounds quarter quarters 2 stone hw hundredweight 4 quarters tl long tons 20 hundredweight ts short tons 2,000 pounds ct carats 200 milligrams gr grains 64.79891 milligrams dwt penny weight 24 grains ozt troy ounces 20 penny weight lbt troy pounds 12 troy ounces 3.3.7 Power CAPTION: Power Units Symbol Name Calculation W SI watts hp mechanical horsepower 745.69987158 watts bhp boiler horsepower 9,809.5 watts ehp electrical horsepower 746.0 watts mhp metric horsepower 735.49875 watts 3.3.8 Pressure CAPTION: Pressure Units Symbol Name Calculation Pa SI pascals at technical atmospheres 98.0665 kilopascals atm standard atmospheres 101,325 pascals Torr torrs 1÷760 = 1.315789×10^-3 standard atmospheres bar bars 100,000 pascals psi pounds per square inch 6.894757 kilopascals mmHg millimeters of mercury 133.322387415 pascals inHg inches of mercury 25.4 millimeters of mercury 3.3.9 Speed CAPTION: Speed Units Symbol Name Calculation mps SI meters per second kmph kilometers per hour 1,000 ÷ (60 × 60) mph miles per hour (2.54 × 12 × 5,280) ÷ 100,000 3.3.10 Temperature CAPTION: Temperature Units Symbol Name Calculation DC degrees Celsius K kelvins degrees Celsius + 273.15 DF degrees Fahrenheit degrees Celsius × 5 ÷ 9 + 32 DR degrees Rankine kelvins × 5 ÷ 9 DRé degrees Réaumur 1.25 degrees Celsius DRø degrees Rømer 100÷52.5 = 1.90476 degrees Celsius + 7.5 DDe degrees Delisle −2÷3 = −0.666667 degrees Celsius + 150 DN degrees Newton 100÷33 = 3.0303 degrees Celsius 3.3.11 Time CAPTION: Time Units Symbol Name Calculation s, sec SI seconds min minutes 60 seconds hr hours 60 minutes da days 24 hours wk weeks 7 days sen sennights 7 days fort fortnights 14 days yr years 365.2422 days dec decades 10 years cen centuries 100 years mil millennia 1000 years 3.3.12 Volume CAPTION: Volume Units Symbol Name Calculation m3 SI meters^3 cc cubic centimeters 1 centimeters^3 l SI liters 1 cubic centimeter tsp teaspoons 4.92892 milliliters tbsp tablespoons 3 teaspoons floz fluid ounces 2 tablespoons cup cups 8 fluid ounces pt pints 2 cups qt quarts 2 pints gal gallons 4 quarts cbin cubic inches 2.54^3 = 16.3871 centimeters^3 cbft cubic feet 12^3 = 1728 cubic inches cbyd cubic yards 3^3 = 27 cubic feet cbrd cubic rods 5.5^3 = 166.375 cubic yards cbch cubic chains 4^3 = 64 cubic rods cblink cubic links 0.01^3 = 10^−6 cubic chains cbfur cubic furlongs 10^3 = 1,000 cubic chains cbmi cubic miles 8^3 = 512 cubic furlongs cblg cubic leagues 3^3 = 9 cubic miles 3.4 Système International Prefixes Any of these symbols may be prepended to the symbol for any metric unit, and any of these names may be prepended to the name for any metric unit. The metric units within the unit tables are flagged with SI [Système International]. 3.4.1 For Positive Powers of Ten CAPTION: Prefixes for Positive Powers of Ten Name Symbol Short Scale Long Scale 10^1 deca da ten ten 10^2 hecto h hundred hundred 10^3 kilo k thousand thousand 10^6 mega M million million 10^9 giga G billion milliard 10^12 tera T trillion billion 10^15 peta P quadrillion billiard 10^18 exa E quintillion trillion 10^21 zetta Z sextillion trilliard 10^24 yotta Y septillion quadrillion 3.4.2 For Negative Powers of Ten Note u (rather than µ) is being used for micro. CAPTION: Prefixes for Negative Powers of Ten Name Symbol Short Scale Long Scale 10^−1 deci d tenth tenth 10^−2 centi c hundredth hundredth 10^−3 milli m thousandth thousandth 10^−6 micro u millionth millionth 10^−9 nano n billionth milliardth 10^−12 pico p trillionth billionth 10^−15 femto f quadrillionth billiardth 10^−18 atto a quintillionth trillionth 10^−21 zepto z sextillionth trilliardth 10^−24 yocto y septillionth quadrillionth 3.4.3 For Positive Powers of Two CAPTION: Prefixes for Positive Powers of Two Name Symbol 2^10 kibi Ki 2^20 mebi Mi 2^30 gibi Gi 2^40 tebi Ti 2^50 pebi Pi 2^60 exbi Ei 2^70 zebi Zi 2^80 yobi Yi