Can water be softened after boiling?

Hi,

I have a problem wish my dish washer after changing the supply from
soft cold water to soft hard water (as I don't have a water softener
other than the dish washer's built-in one), because I wish to save
money by using natural gas to heat the water instead of electricity.

My plates and glasses have a very thick layer of CaCO3 deposited on
them (which can be removed with lemon juice, but thats just not
convenient), yet the salt container is full of NaCl (to be specific
99.9% NaCl supplied by British Salt under the tradename Granulite
http://www.british-salt.co.uk/products/specs/gran_spec.htm)

Please can someone explain the chemical reaction that replaces Ca ions
with Na ions to remove the "hardness"?

Must the NaCl be applied to the CaHCO3 before the natural gas boiler
causes the CaCO3 to be precipitated? (i.e. Do I need to buy a water
softener/conditioner and install it before the boiler?)

Thanks to anyone who can help,
Ken.

.

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