How to convert a wide voltage range (1 V-12 V) to 5 V?
Allow me to make this circuit suggestion:







simulate this circuit &ndash; Schematic created using CircuitLab

For 1 V &lt; Vin &lt; 6 V the boost converter converts to a 6 V internal voltage and the LDO regulates that 6 V down to 5 V

For 6 V &lt; Vin &lt; 12 V the voltage at the Boost converter's output will "follow" the input voltage with some voltage drop due to a (Schottky) diode, so Vin = 7 V => Vmid = 6.5 V and Vin = 12 V => Vmid = 11.5 V.

Remember that boost converters have this basic circuit:



So when Vin is higher than the configured (regulated) output voltage, the output will follow the input voltage with a voltage drop from the coil's resistance and the diode.