# `ᵇ` — Bitwise

Monadic operator. Keys: `Alt-6 b`. Hanzi: `按`

`fᵇ` applies the Boolean function `f` separately to each bit of its
integer arguments. Negative integers use infinite two’s complement.

``` bpl
6∧ᵇ3               ⍝ 2ₓ
6∨ᵇ3               ⍝ 7ₓ
6≠ᵇ3               ⍝ 5ₓ
~ᵇ6                ⍝ ¯7ₓ
```

Arguments follow the usual [integer
conversion](../numbers.qmd#exact-and-approximate), including
whole-valued floats such as bare `6`. Results are exact integers, or
Booleans when every argument is Boolean. Agreement is pervasive.

``` bpl
6 3∧ᵇ5             ⍝ [4 1]ₓ
$t∧ᵇ$f             ⍝ $f
```

For a monadic call, `f` is evaluated on `$f` and `$t`. For a dyadic
call, it is evaluated on all four Boolean pairs. Each evaluation must
return one Boolean value. The operand can be any function or composition
that satisfies this rule.

`ᵇ` is an ordinary monadic operator. It requires a function operand.
Differentiation is unsupported.

In Python, `f.bitwise` constructs `fᵇ`. Array and Function `&`, `|` and
`~` use `∧ᵇ`, `∨ᵇ` and `~ᵇ`. Plain BPL `∧` and `∨` retain LCM and GCD.