A fixed point is a value that maps to itself, x* = f(x*), so substituting it back in leaves the state unchanged. It is the discrete-map analog of an equilibrium: once there, the system stays. The exact closure holds only for the stated map; real systems add noise, parameter drift, and model error, so a computed fixed point is only as trustworthy as the map behind it.
A fixed point is a checked finite substitution. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Fixed point means the update returns itself
The candidate one half is checked by substitution.
f(21)=21⋅21+41=21
The fixed bit is computed, not chosen
Because the output is again one half, the fixed bit is 1.