Choose source base 2 and enter -101010. The minus is separated before digit validation; every remaining character is 0 or 1. NumberBase converts the magnitude exactly, then reapplies the sign. It does not interpret the bits as a fixed-width two's-complement word.
Binary magnitude 101010 equals 42
The one-bits occupy positions 5, 3, and 1: 2⁵ + 2³ + 2¹ = 32 + 8 + 2 = 42. Left-to-right accumulation reaches the same result through repeated multiply-by-2 and add-digit steps.
Apply the sign after exact accumulation
The magnitude BigInt is 42, so the complete value is -42. Rendering keeps one leading minus: base 2 -101010, base 8 -52, base 10 -42, base 16 -2A, and base 36 -16. None is a bitwise encoding of a negative machine word.
Bit width is deliberately absent
Two's-complement output depends on choosing a width such as 8, 16, 32, or 64 bits and deciding overflow behavior. This integer converter asks for neither, so sign-and-magnitude text is the only unambiguous cross-base result. Binary arithmetic encoding belongs to a different tool contract.