--- layout: default title: "Bits" parent: Composite ancestor: Funcons-beta --- [Funcons-beta] : [Bits.cbs] ----------------------------- ### Bits and bit vectors

[
  Type     bits
  Datatype bit-vectors
  Funcon   bit-vector
  Type     bytes             Alias octets
  Funcon   bit-vector-not
  Funcon   bit-vector-and
  Funcon   bit-vector-or
  Funcon   bit-vector-xor
  Funcon   bit-vector-shift-left
  Funcon   bit-vector-logical-shift-right
  Funcon   bit-vector-arithmetic-shift-right
  Funcon   integer-to-bit-vector
  Funcon   bit-vector-to-integer
  Funcon   bit-vector-to-natural
  Funcon   unsigned-bit-vector-maximum
  Funcon   signed-bit-vector-maximum
  Funcon   signed-bit-vector-minimum
  Funcon   is-in-signed-bit-vector
  Funcon   is-in-unsigned-bit-vector
]

#### Bits

Type
  bits ~> booleans

false represents the absence of a bit, true its presence. #### Bit vectors

Datatype
  bit-vectors(N:natural-numbers) ::= bit-vector(_:bits^N)

Type
  bytes ~> bit-vectors(8)
Alias
  octets = bytes

Meta-variables
  BT <: bit-vectors(_)

Built-in Funcon
  bit-vector-not(_:BT) : =>BT

Built-in Funcon
  bit-vector-and(_:BT, _:BT) : =>BT

Built-in Funcon
  bit-vector-or(_:BT, _:BT) : =>BT

Built-in Funcon
  bit-vector-xor(_:BT, _:BT) : =>BT

The above four funcons are the natural extensions of funcons from booleans to bit-vectors(N) of the same length.

Built-in Funcon
  bit-vector-shift-left(_:BT, _:natural-numbers) : BT

Built-in Funcon
  bit-vector-logical-shift-right(_:BT, _:natural-numbers) : BT

Built-in Funcon
  bit-vector-arithmetic-shift-right(_:BT, _:natural-numbers) : BT

Built-in Funcon
  integer-to-bit-vector(_:integers, N:natural-numbers) : bit-vectors(N)

integer-to-bit-vector(M, N) converts an integer M to a bit-vector of length N, using Two's Complement representation. If the integer is out of range of the representation, it will wrap around (modulo 2^N).

Built-in Funcon
  bit-vector-to-integer(_:BT) : =>integers

bit-vector-to-integer(B) interprets a bit-vector BV as an integer in Two's Complement representation.

Built-in Funcon
  bit-vector-to-natural(_:BT) : =>natural-numbers

bit-vector-to-natural(BV) interprets a bit-vector BV as a natural number in unsigned representation.

Funcon
  unsigned-bit-vector-maximum(N:natural-numbers) : =>natural-numbers
    ~> integer-subtract(integer-power(2, N), 1)

Funcon
  signed-bit-vector-maximum(N:natural-numbers) : =>integers
    ~> integer-subtract(integer-power(2, integer-subtract(N, 1)), 1)

Funcon
  signed-bit-vector-minimum(N:natural-numbers) : =>integers
    ~> integer-negate(integer-power(2, integer-subtract(N, 1)))

Funcon
  is-in-signed-bit-vector(M:integers, N:natural-numbers) : =>booleans
    ~> and(integer-is-less-or-equal(M, signed-bit-vector-maximum(N)),
           integer-is-greater-or-equal(M, signed-bit-vector-minimum(N)))

Funcon
  is-in-unsigned-bit-vector(M:integers, N:natural-numbers) : =>booleans
    ~> and(integer-is-less-or-equal(M, unsigned-bit-vector-maximum(N)),
           integer-is-greater-or-equal(M, 0))

____ From the [PLanCompS Project] | [CBS-beta issues...] | [Suggest an improvement...] [Bits.cbs]: Bits.cbs "CBS SOURCE FILE" [Funcons-beta]: /CBS-beta/docs/Funcons-beta "FUNCONS-BETA" [Unstable-Funcons-beta]: /CBS-beta/docs/Unstable-Funcons-beta "UNSTABLE-FUNCONS-BETA" [Languages-beta]: /CBS-beta/docs/Languages-beta "LANGUAGES-BETA" [Unstable-Languages-beta]: /CBS-beta/docs/Unstable-Languages-beta "UNSTABLE-LANGUAGES-BETA" [CBS-beta]: /CBS-beta "CBS-BETA" [PLanCompS Project]: https://plancomps.github.io "PROGRAMMING LANGUAGE COMPONENTS AND SPECIFICATIONS PROJECT HOME PAGE" [CBS-beta issues...]: https://github.com/plancomps/CBS-beta/issues "CBS-BETA ISSUE REPORTS ON GITHUB" [Suggest an improvement...]: mailto:plancomps@gmail.com?Subject=CBS-beta%20-%20comment&Body=Re%3A%20CBS-beta%20specification%20at%20Values/Composite/Bits/Bits.cbs%0A%0AComment/Query/Issue/Suggestion%3A%0A%0A%0ASignature%3A%0A "GENERATE AN EMAIL TEMPLATE"