Question

Bike computers tell the ride what altitude they are at and how the altitude is changing using a basic barometer

Answer 1

A typical barometer measures the pressure of the location at where you're at. Once it displays the pressure, you can determine the height using the hydrostatic pressure. The equation is written below:

P = ρgh,
where
ρ is the density of air
g is the acceleration due to gravity
h is the height

Therefore, if the pressure increases, then the height also increases.