Let me apologize for not being clearer and more comprehensive.
On a typical stat the following wires are needed:
R (red) 24V Power (Hot)
**Y ** (yellow) send power out to your A/C unit
W (white) sends power to your gas valve or electric heat etc
G (green) sends power to your fan/blower
**C ** (blue) the “common” side of the 24V power. (more on this wire below)
Your digital programmable thermostat has essentially 2 functions:
1)It keeps Time and [actual] Temperature.
Because those are changing-----and therefore can’t be stored in memory------ it keeps time/temp.
2) It actually switches those wires based on what the thermostat calls for, in some/most cases. (more on that in a minute…)**
So…as an example…if your furnace calls for heat because the space is getting colder, the batteries “throw the switch” that allows the 24V to flow through the stat to the gas valve. The batteries are not operating the furnace directly, although you might say it is indirectly because it is throwing the switch.
So muldoonthief is correct that in his house batteries are required to operate the furnace [indirectly]. muldoonthief may have the 24V available to power up the fan/gas valve/ A/C etc-------- but in his house (and most houses, really…) it is the batteries that throw the switch.
So, no batteries, no furnace, A/C etc.
At the risk of being redundant then, it is accurate to say that dead/weak batteries in a thermostat will cause the furnace or A/C not to work.
There is an exception:
Most digital thermostats have a provision for a “common” wire; the “common” side of the 24V----one is “Hot” (the “R” terminal) and one is “common” (the **“C”**terminal, usually a blue wire)
Do you remember the 2 functions listed above?
Well, when you add the 5th wire----the common wire C/Blue-----the presence of the common wire allows the 24V to [essentially] “take over” the switching function and now the only function left for the batteries is to keep Time/Temp.
So if have the additional wires available and you wire in the Common wire into the stat and the furnace the stat will now work without batteries.
Does that make sense? I hope so.
One last thing…
The program memory is written on an eprom chip (…erasable, permanent memory…, iirc…), so most [reasonably] modern digital stats do not use the batteries to “hold on” to what you programmed.