Group: conditional control
Group: sequences
Topic: conditional expression
Topic: elements
Topic: failure returning functions and expressions
Topic: integer values and operations
Topic: kinds of numbers
Topic: logic
Topic: packed data
Topic: string operations
Topic: strings
Topic: subsequences
Topic: unbounded precision
Topic: undefined, null, and other signal values
 
Summary
A binary number is a base two number. A boolean value is a binary bit. It can represent 0/1, true/false, and yes/no. A bit string is a sequence of binary bits. It is equivalent to a binary number.
Boolean values form a basis for formal logic. Binary numbers are commonly used in computers. A boolean variable may need to change to a multivalued variable. (cbb 4/98)
Subtopic: boolean algebra
Quote: only 0 and 1 satisfy x^2=x; algebra of 0 and 1 is the same as the algebra of logic with a new interpretation [»boolG_1854, OK]
 Quote: Nothing and Universe are the limits of class extension; interpret 0 as Nothing and 1 as Universe [»boolG_1854, OK]
 Quote: example of translating an assertion into Boolean algebra [»boolG_1854, OK]
 Quote: use x=1 for proposition X is true; x=0 for falsehood; xy=1 for proposition X and Y are true together; etc. [»boolG_1854, OK]
 Quote: a false term leads to contradiction; a true term does not
 Quote: can solve virtually all statements with yes/no values [»zuseK_1984]
 Quote: Hobbeseverything done by our mind is a computation; 'is' and 'is not' corresponds to + and  [»leibGW_1666]
 Quote: every proposition is true or false; if L is false, it is nontrue [»leibGW_1686]
 Quote: AnonA is not a thing
 Quote: A=A, nonA=nonA, AA=A, nonnonA=A, if A=B then AC=BC for some C, if A=B then nonA=nonB, if A=B then A!=nonB [»leibGW_1686]
 Quote: it is impossible for anything to be and not to be; the most certain of principles [»aris_322a]
 Quote: laws of form: a crossing made again has a different value [»browGS_1972]
 Subtopic: binary system
Quote: the binary system may be used in place of the decimal system; express all numbers by unity and by nothing [»leibGW_1679]
 Quote: a bit is a binary digit; for measuring information [»shanCE7_1948]
 Note: Harriot, d. 1621, used the binary system many years before Leibnitz
 Quote: one's enough to bring everything out of nothing; binary number system [»leibGW_1697]
 Quote: Leibniz designed the first fourspecies adding machine and other logical artifacts. He invented the binary number system and related algorithms [»kramS2_1996]
 Quote: a computer's arithmetic, control and memory parts should use binary representation; simpler logical structure [»vonnJ6_1945]
 Quote: an electronic computing machine should use the binary system and convert to decimal only for I/O
 Subtopic: boolean program
Quote: Slam turns a C program into a boolean program with the same controlflow and Boolean variables; easier to analyze [»laruJR5_2004]
 Subtopic: bit algorithmes
Quote: bitcounting algorithm based on frequency division; most efficient for sparse vectors [»berkS11_2000]
 Subtopic: bit fields
Quote: two bits of metadata per heap data; delimiter bit and value bit gives size, free and allocated [»kharM10_2006]
 Quote: define bit fields by endian convention, width, low and high bit; generate shifts and masks automatically [»ramsN5_1997]
 Quote: bit fields are better than bit strings for binary representation: order independent, check for overlaps and gaps, specified length
 Quote: bit sequences fit into a computer word for packing and efficient processing; specify max length [»wirtN6_1966]
 Quote: register allocation algorithm for packing multiple subword variables in one register; needed for processors that reference bit sections in registers [»tallS1_2003]
 Subtopic: masked integer
Quote: fast addition, subtraction, and compare of masked integers; i.e., a subset of bits in a computer word [»adamMD5_2006]
 Subtopic: bitvector
Quote: unidirectional bitvector analysis used for liveness, reaching def, defuse, code motion, partial dead code, and strength reduction; works for parallel programs [»knooJ5_1995]
 Quote: bitvector encoding of the nqueen problem; natural, simple, and efficient [»zongQ2_2002]
 Subtopic: 'true' and 'false' value
Quote: 'true' in Smalltalk is any object except for 'false'; the object may be used by the message sender [»goldA3_1976]
 QuoteRef: hallJC5_1974 ;;43 null string acts as success (sxx for side effects)
 QuoteRef: sammJE_1969 ;;459 nil (empty list) is false while all other lists are true so no need logical data type
 QuoteRef: wileDS11_1973 ;;30 'a relation b' returns nil if false otherwise a
 Quote: could define boolean values as 0_1; this removes the need for a characteristic function for predicates [»boutRT1_1990]
 QuoteRef: sammJE_1969 ;;223 function to convert booleans to 1 or O
 Quote: for boolean ('f' tag) variables, describe the condition under which the variable is true; e.g., 'fOpen'
 Quote: the value of a literal is the literal itself; e.g., true, false, and .capOmega. as undefined [»wirtN1_1966]
 Subtopic: status register
Quote: PL.8 intermediate language uses a status register for compares and conditional jumps; no source language control structures [»auslM6_1982]
 Subtopic: boolean operations
Quote: always keep the powersoftwo table and the routine changing sequence (PERM) in memory; the later simplifies call and return from a routine [»turiA3_1951]
 QuoteRef: kuznOP6_1972 ;;958 in Yarus, all variables are boolean; cause all output is boolean on or off
 QuoteRef: seedH_1971 ;;90 indicators for whether the field is +  or 0
 Quote: set the match flag on testing character input; can be tested later [»kherL9_1978]
 QuoteRef: nievJ8_1970 ;;261 all tests recorded in var. T (nalready used across beginend, Ssuccess ffailure, W/wrong:error detected) each begin match argument which on miss match skips unit. each end match arg which repeats(bounces) on miss match (exit guard)
 QuoteRef: ruhlRC11_1976 ;;31 "Two consecutive Logic Outputs may be declared an exclusive pair, whereby if one is turned ON, the other is always automatically turned off.

Related Topics
Group: conditional control (7 topics, 142 quotes)
Group: sequences (7 topics, 97 quotes)
Topic: conditional expression (11 items)
Topic: elements (22 items)
Topic: failure returning functions and expressions (24 items)
Topic: integer values and operations (13 items)
Topic: kinds of numbers (24 items)
Topic: logic (84 items)
Topic: packed data (11 items)
Topic: string operations (20 items)
Topic: strings (13 items)
Topic: subsequences (13 items)
Topic: unbounded precision (9 items)
Topic: undefined, null, and other signal values (34 items)
