⊥ — Decode

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

⊥Y decodes binary digits along the last axis.

⊥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.

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.

3⊥2 4 5            ⍝ 35

Each row of Y holds the digits of one number, as Encode writes them. B⊥B⊤N gives back N when B has enough digits.

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

Inverse

⊥⁻¹ is ⊤.

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