mirror of
https://github.com/QB64Official/qb64.git
synced 2024-09-20 09:04:44 +00:00
510 lines
23 KiB
Text
510 lines
23 KiB
Text
|
{| align="center"
|
|||
|
| __TOC__
|
|||
|
|}
|
|||
|
|
|||
|
==Basic and QB64 Numerical Types==
|
|||
|
<center>'''Qbasic Number Types'''</center>
|
|||
|
|
|||
|
* [[INTEGER]] ['''%''']: 2 Byte signed whole number values from -32768 to 32767. 0 to 65535 unsigned. (currently not checked in QB64)
|
|||
|
* [[LONG]] ['''&''']: 4 byte signed whole number values from -2147483648 to 2147483647. 0 to 4294967295 unsigned.
|
|||
|
* [[SINGLE]] ['''!''']: 4 byte signed floating decimal point values of up to 7 decimal place accuracy. '''Cannot be unsigned!'''
|
|||
|
* [[DOUBLE]] [#]: 8 byte signed floating decimal point values of up to 15 decimal place accuracy. '''Cannot be unsigned!'''
|
|||
|
* To get '''one byte''' values, can use an [[ASCII]] [[STRING]] character to represent values from 0 to 255 as in [[BINARY]] files.
|
|||
|
|
|||
|
|
|||
|
<center>'''QB64 Number Types'''</center>
|
|||
|
|
|||
|
* [[_BIT]] ['''`''']: 1 bit signed whole number values of 0 or -1 signed or 0 or 1 unsigned. [[_BIT]] * 8 can hold a signed or unsigned [[_BYTE|byte]] value.
|
|||
|
* [[_BYTE]] ['''%%''']: 1 byte signed whole number values from -128 to 127. Unsigned values from 0 to 255.
|
|||
|
* [[_INTEGER64]] ['''&&''']: 8 byte signed whole number values from -9223372036854775808 to 9223372036854775807
|
|||
|
* [[_FLOAT]] [##]: currently set as 10 byte signed floating decimal point values up to 1.1897E+4932. '''Cannot be unsigned!'''
|
|||
|
* [[_OFFSET]] [%&]: undefined flexable length integer offset values used in [[DECLARE DYNAMIC LIBRARY]] declarations ONLY.
|
|||
|
|
|||
|
|
|||
|
<center>'''Signed and Unsigned Integer Values'''</center>
|
|||
|
|
|||
|
Negative (signed) numerical values can affect calculations when using any of the BASIC operators. SQR cannot use negative values! There may be times that a calculation error is made using those negative values. The SGN function returns the sign of a value as -1 for negative, 0 for zero and 1 for unsigned positive values. ABS always returns an unsigned value.
|
|||
|
|
|||
|
::::* [[SGN]](n) returns the value's sign as -1 if negative, 0 if zero or 1 if positive.
|
|||
|
::::* [[ABS]](n) changes negative values to the equivalent positive values.
|
|||
|
::::* '''QB64:''' [[_UNSIGNED]] in a [[DIM]], [[AS]] or [[_DEFINE]] statement for only positive [[INTEGER]] values.
|
|||
|
|
|||
|
|
|||
|
::[[_UNSIGNED]] integer, byte and bit variable values can use the tilde ~ suffix before the type suffix to define the type.
|
|||
|
|
|||
|
|
|||
|
<center>[[#toc|Return to Top]]</center>
|
|||
|
|
|||
|
==Mathematical Operation Symbols==
|
|||
|
Most of the BASIC math operators are ones that require no introduction. The addition, subtraction, multplication and division operators are ones commonly used as shown below:
|
|||
|
|
|||
|
{| align="center" border=1
|
|||
|
! Symbol
|
|||
|
! Procedure Type
|
|||
|
! Example Usage
|
|||
|
! Operation Order
|
|||
|
|-
|
|||
|
| align="center" |[[+]] || Addition || align="center" | c = a + b || align="center" | Last
|
|||
|
|-
|
|||
|
| align="center" |[[-]] || Subtraction || align="center" | c = a - b || align="center" | Last
|
|||
|
|-
|
|||
|
| align="center" |[[-]] || Negation || align="center" | c = - a || align="center" | Last
|
|||
|
|-
|
|||
|
| align="center" |[[*]] || Multiplication || align="center" | c = a * b || align="center" | Second
|
|||
|
|-
|
|||
|
| align="center" |[[/]] || Division || align="center" | c = a / b || align="center" | Second
|
|||
|
|}
|
|||
|
|
|||
|
|
|||
|
BASIC can also use two other operators for '''[[INTEGER]] division'''. Integer division returns only whole number values. [[MOD]] '''remainder division''' returns a value only if an integer division cannot divide a number exactly. Returns 0 if a value is exactly divisible.
|
|||
|
|
|||
|
|
|||
|
{| align="center" border=1
|
|||
|
!Symbol
|
|||
|
!Procedure Type
|
|||
|
!Example Usage
|
|||
|
!Operation Order
|
|||
|
|-
|
|||
|
| align="center" |[[\]] || Integer division || align="center" | c = a \ b || align="center" | Second
|
|||
|
|-
|
|||
|
| align="center" |[[MOD]] || Remainder division || align="center" | c = a MOD b || align="center" | Second
|
|||
|
|}
|
|||
|
|
|||
|
|
|||
|
<center>'''''It is an [[ERROR|error]] to divide by zero or to take the remainder modulo zero.'''''</center>
|
|||
|
|
|||
|
|
|||
|
There is also an operator for '''exponential''' calculations. The exponential operator is used to raise a number's value to a designated exponent of itself. In QB the exponential return values are [[DOUBLE]] values. The [[SQR]] function can return a number's Square Root. For other '''exponential roots''' the operator can be used with fractions such as (1 / 3) designating the cube root of a number.
|
|||
|
|
|||
|
|
|||
|
{| align="center" border=1
|
|||
|
!Symbol
|
|||
|
!Procedure
|
|||
|
!Example Usage
|
|||
|
!Operation Order
|
|||
|
|-
|
|||
|
| align="center" |[[^]] || Exponent || align="center" | c = a [[^]] (1 / 2) || align="center" | First
|
|||
|
|-
|
|||
|
| align="center" | [[SQR]] || Square Root || align="center" | c = [[SQR]](a [[^]] 2 + b [[^]] 2) || align="center" | First
|
|||
|
|}
|
|||
|
|
|||
|
|
|||
|
:'''''Note: Exponent fractions should be enclosed in () brackets in order to be treated as a root rather than as division!'''''
|
|||
|
<center> '''Negative exponential values must be enclosed in () brackets with QB64 currently!'''</center>
|
|||
|
|
|||
|
|
|||
|
<center>[[#toc|Return to Top]]</center>
|
|||
|
|
|||
|
==Basic's Order of Operations==
|
|||
|
|
|||
|
When a normal calculation is made, BASIC works from left to right, but it does certain calculations in the following order:
|
|||
|
|
|||
|
|
|||
|
:::# Exponential and exponential Root calculations including [[SQR]].
|
|||
|
:::# Negation (Note that this means that ''- 3 ^ 2'' is treated as ''-(3 ^ 2)'' and not as ''(-3) ^ 2.)''
|
|||
|
:::# Multiplication, normal Division, [[INTEGER]] Division and Remainder([[MOD]]) Division calculations
|
|||
|
:::# Addition and Subtraction calculations
|
|||
|
|
|||
|
|
|||
|
<center>'''Using Parenthesis to Define the Operation Order'''</center>
|
|||
|
|
|||
|
Sometimes a calculation may need BASIC to do them in another order or the calculation will return bad results. BASIC allows the programmer to decide the order of operations by using [[parenthesis]] around parts of the equation. BASIC will do the calculations inside of the [[parenthesis]] brackets first and the others from left to right in the normal operation order.
|
|||
|
|
|||
|
==Basic's Mathematical Functions==
|
|||
|
|
|||
|
{| align=center border=1
|
|||
|
! Function
|
|||
|
! Description
|
|||
|
|-
|
|||
|
| [[ABS]](n) || returns the absolute (positive) value of n: ABS(-5) = 5
|
|||
|
|-
|
|||
|
| [[ATN]](angle*) || returns the arctangent of an angle in radians: π = 4 * ATN(1)
|
|||
|
|-
|
|||
|
| [[COS]](angle*) || returns the cosine of an angle in radians. (horizontal component)
|
|||
|
|-
|
|||
|
| [[EXP]](n) || returns e<sup>x</sup>, '''(n <= 88.02969)''': e = EXP(1) ' (e = 2.718281828459045)
|
|||
|
|-
|
|||
|
| [[LOG]](n) || returns the base e natural logarithm of n. '''(n > 0)'''
|
|||
|
|-
|
|||
|
| [[SGN]](n) || returns -1 if n < 0, 0 if n = 0, 1 if n > 0: SGN(-5) = -1
|
|||
|
|-
|
|||
|
| [[SIN]](angle*) || returns the sine of an angle in radians. (vertical component)
|
|||
|
|-
|
|||
|
| [[SQR]](n) || returns the square root of a number. '''(n >= 0)'''
|
|||
|
|-
|
|||
|
| [[TAN]](angle*) || returns the tangent of an angle in radians
|
|||
|
|}
|
|||
|
|
|||
|
<center> '''* angles measured in radians'''</center>
|
|||
|
|
|||
|
|
|||
|
{{TextStart}} '''Degree to Radian Conversion:'''
|
|||
|
FUNCTION Radian (degrees)
|
|||
|
Radian = degrees * (4 * {{Cb|ATN}}(1)) / 180
|
|||
|
END FUNCTION '' ''
|
|||
|
|
|||
|
FUNCTION Degree (radians)
|
|||
|
Degree = radians * 180 / (4 * {{Cb|ATN}}(1))
|
|||
|
END FUNCTION
|
|||
|
|
|||
|
'''Logarithm to base n'''
|
|||
|
FUNCTION LOGN (X, n)
|
|||
|
IF n > 0 AND n <> 1 AND X > 0 THEN LOGN = {{Cb|LOG}}(X) / {{Cb|LOG}}(n) ELSE BEEP
|
|||
|
END FUNCTION '' ''
|
|||
|
|
|||
|
FUNCTION LOG10 (X) 'base 10 logarithm
|
|||
|
IF X > 0 THEN LOG10 = {{Cb|LOG}}(X) / {{Cb|LOG}}(10) ELSE BEEP
|
|||
|
END FUNCTION '' ''
|
|||
|
{{TextEnd}}
|
|||
|
|
|||
|
|
|||
|
<center>'''The numerical value of n in the [[LOG]](n) evaluation MUST be a positive value!'''</center>
|
|||
|
|
|||
|
<center>'''The numerical value of n in the [[EXP]](n) evaluation MUST be LESS than or equal to 88.02969!'''</center>
|
|||
|
|
|||
|
<center>'''The numerical value of n in the [[SQR]](n) evaluation can NOT be a negative value!'''</center>
|
|||
|
|
|||
|
|
|||
|
<center>[[#toc|Return to Top]]</center>
|
|||
|
|
|||
|
==Derived Mathematical Functions==
|
|||
|
|
|||
|
|
|||
|
The following Trigonometric functions can be derived from the '''BASIC Mathematical Functions''' listed above. Each function checks that certain values can be used without error or a [[BEEP]] will notify the user that a value could not be returned. An error handling routine can be substituted if desired. '''Note:''' Functions requiring '''π''' use 4 * [[ATN]](1) for [[SINGLE]] accuracy. Use [[ATN]](1.#) for [[DOUBLE]] accuracy.
|
|||
|
|
|||
|
|
|||
|
{{TextStart}}'' ''
|
|||
|
FUNCTION SEC (x) 'Secant
|
|||
|
IF COS(x) <> 0 THEN SEC = 1 / {{Cb|COS}}(x) ELSE BEEP
|
|||
|
END FUNCTION
|
|||
|
|
|||
|
FUNCTION CSC (x) 'CoSecant
|
|||
|
IF SIN(x) <> 0 THEN CSC = 1 / {{Cb|SIN}}(x) ELSE BEEP
|
|||
|
END FUNCTION
|
|||
|
|
|||
|
FUNCTION COT (x) 'CoTangent
|
|||
|
IF TAN(x) <> 0 THEN COT = 1 / {{Cb|TAN}}(x) ELSE BEEP
|
|||
|
END FUNCTION
|
|||
|
|
|||
|
FUNCTION ARCSIN (x) 'Inverse Sine
|
|||
|
IF x < 1 THEN ARCSIN = {{Cb|ATN}}(x / {{Cb|SQR}}(1 - (x * x))) ELSE BEEP
|
|||
|
END FUNCTION
|
|||
|
|
|||
|
FUNCTION ARCCOS (x) ' Inverse Cosine
|
|||
|
IF x < 1 THEN ARCCOS = (2 * ATN(1)) - {{Cb|ATN}}(x / {{Cb|SQR}}(1 - x * x)) ELSE BEEP
|
|||
|
END FUNCTION
|
|||
|
|
|||
|
FUNCTION ARCSEC (x) ' Inverse Secant
|
|||
|
IF x < 1 THEN ARCSEC = {{Cb|ATN}}(x / {{Cb|SQR}}(1 - x * x)) + ({{Cb|SGN}}(x) - 1) * (2 * ATN(1)) ELSE BEEP
|
|||
|
END FUNCTION
|
|||
|
|
|||
|
FUNCTION ARCCSC (x) ' Inverse CoSecant
|
|||
|
IF x < 1 THEN ARCCSC = ATN(1 / SQR(1 - x * x)) + (SGN(x)-1) * (2 * ATN(1)) ELSE BEEP
|
|||
|
END FUNCTION
|
|||
|
|
|||
|
FUNCTION ARCCOT (x) ' Inverse CoTangent
|
|||
|
ARCCOT = (2 * {{Cb|ATN}}(1)) - {{Cb|ATN}}(x)
|
|||
|
END FUNCTION '' ''
|
|||
|
|
|||
|
FUNCTION SINH (x) ' Hyperbolic Sine
|
|||
|
IF x <= 88.02969 THEN SINH = ({{Cb|EXP}}(x) - {{Cb|EXP}}(-x)) / 2 ELSE BEEP
|
|||
|
END FUNCTION '' ''
|
|||
|
|
|||
|
FUNCTION COSH (x) ' Hyperbolic CoSine
|
|||
|
IF x <= 88.02969 THEN COSH = (EXP(x) + EXP(-x)) / 2 ELSE BEEP
|
|||
|
END FUNCTION '' ''
|
|||
|
|
|||
|
FUNCTION TANH (x) ' Hyperbolic Tangent or SINH(x) / COSH(x)
|
|||
|
IF 2 * x <= 88.02969 AND EXP(2 * x) + 1 <> 0 THEN
|
|||
|
TANH = ({{Cb|EXP}}(2 * x) - 1) / ({{Cb|EXP}}(2 * x) + 1)
|
|||
|
ELSE BEEP
|
|||
|
END IF
|
|||
|
END FUNCTION '' ''
|
|||
|
|
|||
|
FUNCTION SECH (x) ' Hyperbolic Secant or (COSH(x)) ^ -1
|
|||
|
IF x <= 88.02969 AND (EXP(x) + EXP(-x)) <> 0 THEN SECH = 2 / ({{Cb|EXP}}(x) + {{Cb|EXP}}(-x)) ELSE BEEP
|
|||
|
END FUNCTION '' ''
|
|||
|
|
|||
|
FUNCTION CSCH (x) ' Hyperbolic CoSecant or (SINH(x)) ^ -1
|
|||
|
IF x <= 88.02969 AND (EXP(x) - EXP(-x)) <> 0 THEN CSCH = 2 / ({{Cb|EXP}}(x) - {{Cb|EXP}}(-x)) ELSE BEEP
|
|||
|
END FUNCTION '' ''
|
|||
|
|
|||
|
FUNCTION COTH (x) ' Hyperbolic CoTangent or COSH(x) / SINH(x)
|
|||
|
IF 2 * x <= 88.02969 AND EXP(2 * x) - 1 <> 0 THEN
|
|||
|
COTH = ({{Cb|EXP}}(2 * x) + 1) / ({{Cb|EXP}}(2 * x) - 1)
|
|||
|
ELSE BEEP
|
|||
|
END IF
|
|||
|
END FUNCTION '' ''
|
|||
|
|
|||
|
FUNCTION ARCSINH (x) ' Inverse Hyperbolic Sine
|
|||
|
IF (x * x) + 1 >= 0 AND x + SQR((x * x) + 1) > 0 THEN
|
|||
|
ARCSINH = {{Cb|LOG}}(x + {{Cb|SQR}}(x * x + 1))
|
|||
|
ELSE BEEP
|
|||
|
END IF
|
|||
|
END FUNCTION '' ''
|
|||
|
|
|||
|
FUNCTION ARCCOSH (x) ' Inverse Hyperbolic CoSine
|
|||
|
IF x >= 1 AND x * x - 1 >= 0 AND x + SQR(x * x - 1) > 0 THEN
|
|||
|
ARCCOSH = {{Cb|LOG}}(x + {{Cb|SQR}}(x * x - 1))
|
|||
|
ELSE BEEP
|
|||
|
END IF
|
|||
|
END FUNCTION '' ''
|
|||
|
|
|||
|
FUNCTION ARCTANH (x) ' Inverse Hyperbolic Tangent
|
|||
|
IF x < 1 THEN ARCTANH = {{Cb|LOG}}((1 + x) / (1 - x)) / 2 ELSE BEEP
|
|||
|
END FUNCTION
|
|||
|
|
|||
|
FUNCTION ARCSECH (x) ' Inverse Hyperbolic Secant
|
|||
|
IF x > 0 AND x <= 1 THEN ARCSECH = {{Cb|LOG}}(({{Cb|SGN}}(x) * {{Cb|SQR}}(1 - x * x) + 1) / x) ELSE BEEP
|
|||
|
END FUNCTION '' ''
|
|||
|
|
|||
|
FUNCTION ARCCSCH (x) ' Inverse Hyperbolic CoSecant
|
|||
|
IF x <> 0 AND x * x + 1 >= 0 AND (SGN(x) * SQR(x * x + 1) + 1) / x > 0 THEN
|
|||
|
ARCCSCH = {{Cb|LOG}}(({{Cb|SGN}}(x) * {{Cb|SQR}}(x * x + 1) + 1) / x)
|
|||
|
ELSE BEEP
|
|||
|
END IF
|
|||
|
END FUNCTION '' ''
|
|||
|
|
|||
|
FUNCTION ARCCOTH (x) ' Inverse Hyperbolic CoTangent
|
|||
|
IF x > 1 THEN ARCCOTH = {{Cb|LOG}}((x + 1) / (x - 1)) / 2 ELSE BEEP
|
|||
|
END FUNCTION '' ''
|
|||
|
{{TextEnd}}
|
|||
|
{{WhiteStart}}
|
|||
|
'''Hyperbolic Function Relationships:'''
|
|||
|
|
|||
|
COSH(-x) = COSH(x)
|
|||
|
SINH(-x) = -SINH(x)
|
|||
|
|
|||
|
SECH(-x) = SECH(x)
|
|||
|
CSCH(-x) = -CSCH(x)
|
|||
|
TANH(-x) = -TANH(x)
|
|||
|
COTH(-x) = -COTH(x)
|
|||
|
|
|||
|
'''Inverse Hyperbolic Function Relatonships:'''
|
|||
|
|
|||
|
ARSECH(x) = ARCOSH(x) ^ -1
|
|||
|
ARCSCH(x) = ARSINH(x) ^ -1
|
|||
|
ARCOTH(x) = ARTANH(x) ^ -1
|
|||
|
|
|||
|
'''Hyperbolic sine and cosine satisfy the Pythagorean trig. identity:'''
|
|||
|
|
|||
|
(COSH(x) ^ 2) - (SINH(x) ^ 2) = 1
|
|||
|
|
|||
|
{{WhiteEnd}}
|
|||
|
|
|||
|
<center>[http://support.microsoft.com/kb/28249 Microsoft's Derived BASIC Functions (KB 28249)]</center>
|
|||
|
|
|||
|
|
|||
|
<center>[[#toc|Return to Top]]</center>
|
|||
|
|
|||
|
==Mathematical Logical Operators==
|
|||
|
|
|||
|
: The following logical operators compare numerical values using bitwise operations. The two numbers are compared by the number's [[Binary]] bits on and the result of the operation determines the value returned in decimal form. [[NOT]] checks one value and returns the opposite. It returns 0 if a value is not 0 and -1 if it is 0. See [[Binary]] for more on bitwise operations.
|
|||
|
|
|||
|
|
|||
|
<center>'''Truth table of the 6 BASIC Logical Operators'''</center>
|
|||
|
|
|||
|
|
|||
|
{{Template:LogicalTruthTable}}
|
|||
|
|
|||
|
<center>BASIC can accept any + or - value that is not 0 to be True when used in an evaluation.</center>
|
|||
|
|
|||
|
|
|||
|
<center>[[#toc|Return to Top]]</center>
|
|||
|
|
|||
|
|
|||
|
==Relational Operators==
|
|||
|
Relational Operations are used to compare values in a Conditional [[IF...THEN]], [[SELECT CASE]], [[UNTIL]] or [[WHILE]] statement.
|
|||
|
|
|||
|
|
|||
|
{{Template:RelationalTable}}
|
|||
|
|
|||
|
|
|||
|
<center>[[#toc|Return to Top]]</center>
|
|||
|
|
|||
|
==Basic's Rounding Functions==
|
|||
|
|
|||
|
: Rounding is used when the program needs a certain number value or type. There are 4 [[INTEGER]] or [[LONG]] Integer functions and one function each for closest [[SINGLE]] and closest [[DOUBLE]] numerical types. Closest functions use "bankers" rounding which rounds up if the decimal point value is over one half. Variable types should match the return value.
|
|||
|
|
|||
|
{| align=center border=1
|
|||
|
! Name
|
|||
|
! Description
|
|||
|
|-
|
|||
|
|
|||
|
|[[INT]](n) || rounds down to lower Integer value whether positive or negative
|
|||
|
|-
|
|||
|
|[[FIX]](n) || rounds positive values lower and negative to a less negative Integer value
|
|||
|
|-
|
|||
|
|[[CINT]](n) ||rounds to closest Integer. Rounds up for decimal point values over one half.
|
|||
|
|-
|
|||
|
| [[CLNG]](n) || rounds Integer or Long values to closest value like CINT.(values over 32767)
|
|||
|
|-
|
|||
|
| [[CSNG]](n) || rounds Single values to closest last decimal point value.
|
|||
|
|-
|
|||
|
| [[CDBL]](n) || rounds Double values to closest last decimal point value.
|
|||
|
|-
|
|||
|
| [[_ROUND]] || rounds to closest numerical integer value in '''QB64''' only.
|
|||
|
|}
|
|||
|
|
|||
|
::: '''Note: Each of the above functions define the value's type in addition to rounding the values.'''
|
|||
|
|
|||
|
<center>[[#toc|Return to Top]]</center>
|
|||
|
|
|||
|
==Base Number Systems==
|
|||
|
|
|||
|
|
|||
|
{{TextStart}}
|
|||
|
'''Comparing the [[INTEGER]] Base Number Systems'''
|
|||
|
|
|||
|
'''Decimal (base 10) Binary (base 2) Hexadecimal (base 16) Octal (base 8)'''
|
|||
|
|
|||
|
''' [[&B]] [[&H]] [[HEX$]](n) [[&O]] [[OCT$]](n)'''
|
|||
|
|
|||
|
0 0000 0 0
|
|||
|
1 0001 1 1
|
|||
|
2 0010 2 2
|
|||
|
3 0011 3 3
|
|||
|
4 0100 4 4
|
|||
|
5 0101 5 5
|
|||
|
6 0110 6 6
|
|||
|
7 0111 7 7 -- maxed
|
|||
|
8 1000 8 10
|
|||
|
maxed-- 9 1001 9 11
|
|||
|
10 1010 A 12
|
|||
|
11 1011 B 13
|
|||
|
12 1100 C 14
|
|||
|
13 1101 D 15
|
|||
|
14 1110 E 16
|
|||
|
15 ------------- 1111 <--- Match ---> F ---------------- 17 -- max 2
|
|||
|
16 10000 10 20
|
|||
|
|
|||
|
When the Decimal value is 15, the other 2 base systems are all maxed out!
|
|||
|
The Binary values can be compared to all of the HEX value digit values so
|
|||
|
it is possible to convert between the two quite easily. To convert a HEX
|
|||
|
value to Binary just add the 4 binary digits for each HEX digit place so:
|
|||
|
|
|||
|
F A C E
|
|||
|
&HFACE = 1111 + 1010 + 1100 + 1101 = &B1111101011001101
|
|||
|
|
|||
|
To convert a Binary value to HEX you just need to divide the number into
|
|||
|
sections of four digits starting from the right(LSB) end. If one has less
|
|||
|
than 4 digits on the left end you could add the leading zeros like below:
|
|||
|
|
|||
|
&B101011100010001001 = 0010 1011 1000 1000 1001
|
|||
|
hexadecimal = 2 + B + 8 + 8 + 9 = &H2B889
|
|||
|
|
|||
|
See the Decimal to Binary conversion function that uses '''[[HEX$]]''' on the '''[[&H]]''' page.
|
|||
|
|
|||
|
{{TextEnd}}
|
|||
|
|
|||
|
|
|||
|
<center>'''[[VAL]] converts [[STRING|string]] numbers to Decimal values.'''</center>
|
|||
|
|
|||
|
:VAL reads the string from left to right and converts numerical string values, - and . to decimal values until it finds a character other than those 3 characters. Commas are NOT read either! However HEXadecimal and OCTal base values can be read with [[&H]] or [[&O]].
|
|||
|
|
|||
|
<center>'''The [[OCT$]] [[STRING|string]] function return can be converted to a decimal value using [[VAL]]("&O" + OCT$(n)).'''</center>
|
|||
|
|
|||
|
<center>'''The [[HEX$]] [[STRING|string]] function return can be converted to a decimal value using [[VAL]]("&H" + HEX$(n)).'''</center>
|
|||
|
|
|||
|
|
|||
|
:[[STR$]] converts numerical values to string characters for [[PRINT]] or variable strings. It also removes the right number PRINT space.
|
|||
|
|
|||
|
|
|||
|
|
|||
|
<center>[[#toc|Return to Top]]</center>
|
|||
|
==Bits and Bytes==
|
|||
|
|
|||
|
<center>'''[[_BIT|BITS]]'''</center>
|
|||
|
* The '''MSB''' is the most significant(largest) bit value and '''LSB''' is the least significant bit of a binary or register memory address value. The order in which the bits are read determines the binary or decimal byte value. There are two common ways to read a byte:
|
|||
|
|
|||
|
:* '''"Big-endian"''': MSB is the first bit encountered, decreasing to the LSB as the last bit by position, memory address or time.
|
|||
|
:* '''"Little-endian"''': LSB is the first bit encountered, increasing to the MSB as the last bit by position, memory address or time.
|
|||
|
{{WhiteStart}}
|
|||
|
'''Offset or Position: 0 1 2 3 4 5 6 7 Example: 11110000'''
|
|||
|
---------------------------------- --------
|
|||
|
'''Big-Endian Bit On Value:''' 128 64 32 16 8 4 2 1 240
|
|||
|
'''Little-Endian Bit On Value:''' 1 2 4 8 16 32 64 128 15
|
|||
|
{{WhiteEnd}}
|
|||
|
::The big-endian method compares exponents of 2 <sup>7</sup> down to 2 <sup>0</sup> while the little-endian method does the opposite.
|
|||
|
|
|||
|
<center>'''[[_BYTE|BYTES]]'''</center>
|
|||
|
* [[INTEGER]] values consist of 2 bytes called the '''HI''' and '''LO''' bytes. Anytime that the number of binary digits is a multiple of 16 (2bytes, 4 bytes, etc.) and the HI byte's MSB is on(1), the value returned will be negative. Even with [[SINGLE]] or [[DOUBLE]] values!
|
|||
|
{{WhiteStart}} '''16 BIT INTEGER OR REGISTER'''
|
|||
|
'''AH (High Byte Bits) AL (Low Byte Bits)'''
|
|||
|
BIT: 15 14 13 12 11 10 9 8 | 7 6 5 4 3 2 1 0
|
|||
|
---------------------------------------|--------------------------------------
|
|||
|
HEX: 8000 4000 2000 1000 800 400 200 100 | 80 40 20 10 8 4 2 1
|
|||
|
|
|
|||
|
DEC: -32768 16384 8192 4096 2048 1024 512 256 | 128 64 32 16 8 4 2 1
|
|||
|
{{WhiteEnd}}
|
|||
|
::The HI byte's '''MSB''' is often called the '''sign''' bit! When the highest bit is on, the signed value returned will be negative.
|
|||
|
|
|||
|
|
|||
|
''Example:'' Program displays the bits on for any integer value between -32768 and 32767 or &H80000 and &H7FFF.
|
|||
|
{{CodeStart}} '' ''
|
|||
|
{{Cl|DEFINT}} A-Z
|
|||
|
{{Cl|SCREEN (statement)|SCREEN}} 12
|
|||
|
{{Cl|COLOR}} 11: {{Cl|LOCATE}} 10, 2
|
|||
|
{{Cl|PRINT}} " AH (High Register Byte Bits) AL (Low Register Byte Bits)"
|
|||
|
{{Cl|COLOR}} 14: {{Cl|LOCATE}} 11, 2
|
|||
|
{{Cl|PRINT}} " 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0"
|
|||
|
{{Cl|COLOR}} 13: {{Cl|LOCATE}} 14, 2
|
|||
|
{{Cl|PRINT}} " {{Cl|&H}}8000 4000 2000 1000 800 400 200 100 80 40 20 10 8 4 2 {{Cl|&H}}1"
|
|||
|
{{Cl|COLOR}} 11: {{Cl|LOCATE}} 15, 2
|
|||
|
{{Cl|PRINT}} "-32768 16384 8192 4096 2048 1024 512 256 128 64 32 16 8 4 2 1"
|
|||
|
{{Cl|FOR...NEXT|FOR}} i = 1 {{Cl|TO}} 16
|
|||
|
{{Cl|CIRCLE}} (640 - (37 * i), 189), 8, 9 'place bit circles
|
|||
|
{{Cl|NEXT}}
|
|||
|
{{Cl|LINE}} (324, 160)-(326, 207), 11, BF 'line splits bytes
|
|||
|
{{Cl|DO}}
|
|||
|
{{Cl|IF}} Num {{Cl|THEN}}
|
|||
|
{{Cl|FOR...NEXT|FOR}} i = 15 {{Cl|TO}} 0 {{Cl|STEP}} -1
|
|||
|
{{Cl|IF}} (Num {{Cl|AND}} 2 ^ i) {{Cl|THEN}}
|
|||
|
{{Cl|PAINT}} (640 - (37 * (i + 1)), 189), 12, 9
|
|||
|
Bin$ = Bin$ + "1"
|
|||
|
{{Cl|ELSE}}
|
|||
|
{{Cl|PAINT}} (640 - (37 * (i + 1)), 189), 0, 9
|
|||
|
Bin$ = Bin$ + "0"
|
|||
|
{{Cl|END IF}}
|
|||
|
{{Cl|NEXT}}
|
|||
|
{{Cl|COLOR}} 10: {{Cl|LOCATE}} 16, 50: {{Cl|PRINT}} "Binary ="; {{Cl|VAL}}(Bin$)
|
|||
|
{{Cl|COLOR}} 9: {{Cl|LOCATE}} 16, 10: {{Cl|PRINT}} "Decimal ="; Num;: {{Cl|COLOR}} 13: {{Cl|PRINT}} " Hex = "; Hexa$
|
|||
|
Hexa$ = "": Bin$ = ""
|
|||
|
{{Cl|END IF}}
|
|||
|
{{Cl|COLOR}} 14: {{Cl|LOCATE}} 17, 15: {{Cl|INPUT}} "Enter a decimal or HEX({{Cl|&H}}) value (0 Quits): ", frst$
|
|||
|
first = {{Cl|VAL}}(frst$)
|
|||
|
{{Cl|IF}} first {{Cl|THEN}}
|
|||
|
{{Cl|LOCATE}} 17, 15: {{Cl|PRINT}} {{Cl|SPACE$}}(55)
|
|||
|
{{Cl|COLOR}} 13: {{Cl|LOCATE}} 17, 15: {{Cl|INPUT}} "Enter a second value: ", secnd$
|
|||
|
second = {{Cl|VAL}}(secnd$)
|
|||
|
{{Cl|LOCATE}} 17, 10: {{Cl|PRINT}} {{Cl|SPACE$}}(69)
|
|||
|
{{Cl|END IF}}
|
|||
|
Num = first + second
|
|||
|
Hexa$ = "{{Cl|&H}}" + {{Cl|HEX$}}(Num)
|
|||
|
{{Cl|LOOP}} {{Cl|UNTIL}} first = 0 {{Cl|OR (boolean)|OR}} Num > 32767 {{Cl|OR (boolean)|OR}} Num < -32767
|
|||
|
{{Cl|COLOR}} 11: {{Cl|LOCATE}} 28, 30: {{Cl|PRINT}} "Press any key to exit!";
|
|||
|
{{Cl|SLEEP}}
|
|||
|
{{Cl|SYSTEM}} '' ''
|
|||
|
{{CodeEnd}}
|
|||
|
{{small|Code by Ted Weissgerber}}
|
|||
|
|
|||
|
|
|||
|
<center>[[#toc|Return to Top]]</center>
|
|||
|
|
|||
|
==OFFSET==
|
|||
|
|
|||
|
* [[_OFFSET (function)]] returns the memory offset position as a flexible sized value for a designated variable. See [[Using _OFFSET]].
|
|||
|
|
|||
|
|
|||
|
<center>'''Warning: [[_OFFSET]] values cannot be reassigned to other variable [[TYPE|types]]!'''</center>
|
|||
|
|
|||
|
|
|||
|
<center>'''[[_OFFSET]] values can currently only be used in conjunction with [[_MEM]]ory and [[DECLARE DYNAMIC LIBRARY]] procedures.'''</center>
|
|||
|
|
|||
|
==References==
|
|||
|
''See also:''
|
|||
|
* [[_OFFSET]], [[_MEM]]
|
|||
|
* [[DIM]], [[_DEFINE]]
|
|||
|
* [[TYPE]]
|
|||
|
|
|||
|
{{PageNavigation}}
|