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Boolean programming and bit operations

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    This chapter looks at Boolean programming, Boolean logic, and bit operations.

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    This subchapter is a stub section. It will be filled in with instructional material later. For now it serves the purpose of a place holder for the order of instruction.

    Professors are invited to give feedback on both the proposed contents and the propsed order of this text book. Send commentary to Milo, PO Box 1361, Tustin, California, 92781, USA.

Boolean programming and bit operations

    This chapter looks at Boolean programming, Boolean logic, and bit operations.

    Boolean algebra is named for George Boole, who introduced the ideas in the 1854 work “An Investigation of the Law of Thought”. Claude Shannon showed the application of Boolean algebra to switching circuits in the 1938 work “Symbolic Analysis of Relay and Switching Circuits”.

    Please note the differences between a logical Boolean operation, an integer Boolean operation, and a bit-wise Boolean operation. Note that terminology varies, so you will eventually see references using these terms different than presented here.

    In the case of a logical Boolean operation, the result is a logical BOOLEAN type of either TRUE or FALSE. Some languages, such as C, do not have a built-in Boolean type. There are several different and incompatible encodings for TRUE and FALSE (see table below).

    In the case of an integer Boolean operation, the operation is performed on the two integers as whole numbers. The result can be inaccurate if the integer is not in a specified form (the legal options usually being [ZERO and ONE] or [ZERO and NEGATIVE ONE]. This works best with -1 and 0 as TURE and FALSE (or vice versa). There are several different and incompatible encodings for TRUE and FALSE (see table below).

some
languages
 TRUE FALSE
C 1 0
C non-zero zero
  negative zero or
positive
  -1 0
  0 1

    in the case of a bit-wise Boolean operation, a logical operation is performed on each corresponding bit of the two bit strings (or two single bits). Note that a NOT is performed on only a single bit string or single bit.

Stanford C essentials

    Stanford CS Education Library This [the following section until marked as end of Stanford University items] is document #101, Essential C, in the Stanford CS Education Library. This and other educational materials are available for free at http://cslibrary.stanford.edu/. This article is free to be used, reproduced, excerpted, retransmitted, or sold so long as this notice is clearly reproduced at its beginning. Copyright 1996-2003, Nick Parlante, nick.parlante@cs.stanford.edu.

Bitwise Operators

    C includes operators to manipulate memory at the bit level. This is useful for writing lowlevel hardware or operating system code where the ordinary abstractions of numbers, characters, pointers, etc.… are insufficient -- an increasingly rare need. Bit manipulation code tends to be less “portable”. Code is “portable” if with no programmer intervention it compiles and runs correctly on different types of computers. The bitwise operations are typically used with unsigned types. In particular, the shift operations are guaranteed to shift 0 bits into the newly vacated positions when used on unsigned values.

~      Bitwise Negation (unary) flip 0 to 1 and 1 to 0 throughout
&      Bitwise And
|      Bitwise Or
^      Bitwise Exclusive Or
>>      Right Shift by right hand side (RHS) (divide by power of 2)
<<      Left Shift by RHS (multiply by power of 2)

    Do not confuse the Bitwise operators with the logical operators. The bitwise connectives are one character wide (&, |) while the boolean connectives are two characters wide (&&, ||). The bitwise operators have higher precedence than the boolean operators. The compiler will never help you out with a type error if you use & when you meant &&. As far as the type checker is concerned, they are identical-- they both take and produce integers since there is no distinct boolean type.

    Stanford CS Education Library This [the above section] is document #101, Essential C, in the Stanford CS Education Library. This and other educational materials are available for free at http://cslibrary.stanford.edu/. This article is free to be used, reproduced, excerpted, retransmitted, or sold so long as this notice is clearly reproduced at its beginning. Copyright 1996-2003, Nick Parlante, nick.parlante@cs.stanford.edu.

end of Stanford C essentials

Ada

    “31 Every object in the language has a type, which characterizes a set of values and a set of applicable operations. The main classes of types are elementary types (comprising enumeration, numeric, and access types) and composite types (including array and record types).” —:Ada-Europe’s Ada Reference Manual: Introduction: Language Summary See legal information

    “32/2 An enumeration type defines an ordered set of distinct enumeration literals, for example a list of states or an alphabet of characters. The enumeration types Boolean, Character, Wide_Character, and Wide_Wide_Character are predefined.” —:Ada-Europe’s Ada Reference Manual: Introduction: Language Summary See legal information

JOVIAL

    The following material is from the unclassified Computer Programming Manual for the JOVIAL (J73) Language, RADC-TR-81-143, Final Technical Report of June 1981.

    1.1.5 Built-In Functions

    The JOVIAL built-in functions provide advanced, specialized
    operations that are not covered by the JOVIAL operators.

         BIT(b,i,n)     A string of n bits starting at the i'th bit
                        of the bit string b

         SHIFTL(b,n)    Bit string b shifted left by n bits
         SHIFTR(b,n)    Bit string b shifted right by n bits

    Chapter 1 Introduction, page 9

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    †UNIX used as a generic term unless specifically used as a trademark (such as in the phrase “UNIX certified”). UNIX is a registered trademark in the United States and other countries, licensed exclusively through X/Open Company Ltd.

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    Copyright © 2010, 2012 Milo

    Created: December 5, 2010

    Last Updated: September 29, 2012


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