Don't clear input when switching modes

Problem Statement Often I need to use functions from both programmer and scientific modes in the same calculation, but if I switch modes it loses my input. When the input is representable in both modes there is no reason to clear it.

Evidence or User Insights No other calculator does this, and there's no need for the input to be cleared. There's a button to clear the input.

Proposal Preserve the value when it is within the domain of the target mode, otherwise show an error in the display area.

Goals Remove the annoyance of losing the value when you switch modes.

Non-Goals Settle on a unified representation of values such that separate "modes" are not even necessary.