# `⊥` — Decode

Keys: `Alt-b`. Ranks: `1` monadic, `1 1` dyadic

`⊥Y` decodes binary digits along the last axis.

``` bpl
⊥1 0 1 0          ⍝ 10
```

`B⊥Y` evaluates digits `Y` in base(s) `B`. A unit base extends to every
digit. The first entry of a mixed base is unused.

``` bpl
2⊥1 0 1 0          ⍝ 10
[0 60 60]ₓ⊥[1 1 1]ₓ ⍝ 3661ₓ
```

For coefficient vector `C`, `X⊥C` evaluates the polynomial in descending
powers.

``` bpl
3⊥2 4 5            ⍝ 35
```

Each row of `Y` holds the digits of one number, as [Encode](encode.qmd)
writes them. `B⊥B⊤N` gives back `N` when `B` has enough digits.

``` bpl
2⊥[1 0 1⋄0 1 1]   ⍝ 5 3
2 2 2⊥2 2 2⊤3 5     ⍝ 3 5
```

## Inverse

`⊥⁻¹` is `⊤`.

``` bpl
⊥⁻¹5         ⍝ 1 0 1
24 60⊥⁻¹90   ⍝ 1 30
```