Binary

Binary is the base 2 numbering system. It is used by computers because the computer consists of switches that are either on or off. The primary purpose of reading bit values is to translate what was sent by a port or register read.

• Base 2 has numerical values of 0 for off or 1 for on. There is no QBasic function to return the binary values.
• A computer register has 8 bit switches for one byte of data. Each register can return values from 0 to 255 just like ASCII.
• Each bit can be read by using an exponent of 2 from 0 to 128(2 ^ 0 to 2 ^ 7) utilizing the AND numerical operator.
• Bit numbers and parallel port pins are designated as exponents of 2 also for clarity.
• The first bit(2 ^ 0) of one byte is called the least significant bit(LSB).
• The highest bit(2 ^ 7) of one byte is called the most significant bit(MSB).
• A four bit reading or writing mode is called a nibble mode.

Decimal Bit values returned when a bit is on:

Template:WhiteStart Exponent of 2 and Bit # 7 6 5 4 3 2 1 0

                      Bit 0 = 2 ^ 0 = 1 decimal    binary = 0 0 0 0 0 0 0 1
                      Bit 1 = 2 ^ 1 = 2 decimal    binary = 0 0 0 0 0 0 1 0
                      Bit 2 = 2 ^ 2 = 4 decimal    binary = 0 0 0 0 0 1 0 0
                      Bit 3 = 2 ^ 3 = 8 decimal    binary = 0 0 0 0 1 0 0 0
                      Bit 4 = 2 ^ 4 = 16 decimal   binary = 0 0 0 1 0 0 0 0
                      Bit 5 = 2 ^ 5 = 32 decimal   binary = 0 0 1 0 0 0 0 0
                      Bit 6 = 2 ^ 6 = 64 decimal   binary = 0 1 0 0 0 0 0 0
                      Bit 7 = 2 ^ 7 = 128 decimal  binary = 1 0 0 0 0 0 0 0

                      All_Bits_On = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 = 255

Explanation: The table above only displays the binary value of each bit when on. If a value of 255 was read, the binary number = 11111111 (all bits on). If only bits 2, 3 and 4 are on then the value would be 4 + 8 + 16 = 28 or 00011100.

Truth table of the BASIC Logical Operators:

Table 4: The logical operations and its results. In this table, A and B are the Expressions to invert or combine. Both may be results of former Boolean evaluations. ┌────────────────────────────────────────────────────────────────────────┐ │ Logical Operations │ ├───────┬───────┬───────┬─────────┬────────┬─────────┬─────────┬─────────┤ │ A │ B │ NOT B │ A AND B │ A OR B │ A XOR B │ A EQV B │ A IMP B │ ├───────┼───────┼───────┼─────────┼────────┼─────────┼─────────┼─────────┤ │ true │ true │ false │ true │ true │ false │ true │ true │ ├───────┼───────┼───────┼─────────┼────────┼─────────┼─────────┼─────────┤ │ true │ false │ true │ false │ true │ true │ false │ false │ ├───────┼───────┼───────┼─────────┼────────┼─────────┼─────────┼─────────┤ │ false │ true │ false │ false │ true │ true │ false │ true │ ├───────┼───────┼───────┼─────────┼────────┼─────────┼─────────┼─────────┤ │ false │ false │ true │ false │ false │ false │ true │ true │ └───────┴───────┴───────┴─────────┴────────┴─────────┴─────────┴─────────┘ Note: In most BASIC languages incl. QB64 these are bitwise operations, hence the logic is performed for each corresponding bit in both operators, where true or false indicates whether a bit is set or not set. The outcome of each bit is then placed into the respective position to build the bit pattern of the final result value. As all Relational Operations return negative one (-1, all bits set) for true and zero (0, no bits set) for false, this allows us to use these bitwise logical operations to invert or combine any relational checks, as the outcome is the same for each bit and so always results into a true (-1) or false (0) again for further evaluations.

Explanation: The Logical Operators can be used to change bit values of a byte when comparing them to another byte value. AND can determine if each bit is on using a comparison with exponents of 2 from 0 to 7. OR can turn on a bit only when at least one bit is on in a comparison. It cannot turn off a bit! XOR can switch bits on if only ONE of the values has a bit on. Not both! These 3 logical operators are often used to work with register or port readings to turn bits on or off.

Example 1: Converting decimal values to a string binary value. Use LOCATE before the SUB call to locate the PRINT.

DO LOCATE 2, 10 INPUT "Enter a numerical value to convert to binary(0 quits): ", decimal& CLS: LOCATE 10, 10 Decimal2Binary (decimal&) 'pass number by value using parenthesis LOOP UNTIL decimal& = 0 END SUB Decimal2Binary(number&) IF number& = 0 THEN EXIT SUB DO remain% = ABS(number& MOD 2) ' remainder is used to create binary number number& = number& \ 2 ' move up one exponent of 2 with integer division Bin$ = LTRIM$(STR$(remain%)) ' make remainder a string number Binary$ = Bin$ + Binary$ ' add remainder to binary number LOOP UNTIL number& = 0 PRINT "Binary number = " + Binary$ 'binary result END SUB

Explanation: Displays Binary bits on as 1. Remainder can only be 1 or 0 in each loop. Can return all positive values correctly. The decimal parameter could come from a register return value read by INP(address) and 1 would indicate the pins or bits on.

Example 2: Turning flip-flop BIT flags on or off and determining the bits on in a BYTE of program data.

_DEFINE B AS _UNSIGNED _BYTE 'unsigned allows byte values from 128 to 255 PRINT "Hit number keys 1 to 8 to turn flags ON or OFF" DO a$ = INKEY$ 'get bit numbers 1 through 8 only k = VAL(a$) IF k > 0 AND k < 9 THEN 'test for switch on or off bitval = 2 ^ (k - 1) IF (byte AND bitval) = 0 THEN byte = byte + bitval ELSE byte = byte - bitval LOCATE 10, 10: PRINT "Switches on:"; FOR i = 0 TO 7 'maximum byte value is 255 IF (byte AND 2 ^ i) THEN PRINT i + 1; NEXT PRINT "Byte ="; byte; SPACE$(4) END IF LOOP UNTIL _KEYDOWN(27) SLEEP SYSTEM

Code by Ted Weissgerber

Explanation: The byte value is checked to see if the switch is already on. If it is not on, then the bit value is turned on by adding that value to the byte value. If it is on, that value is subtracted. The FOR...NEXT loop reads each bit and displays the switches on.

See also:

• _BIT, &B, _BYTE
• _SHL, _SHR
• AND, OR, XOR, EQV, IMP
• BINARY(file mode), DO...LOOP
• FOR...NEXT, Boolean
• Mathematical Operations

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