Linking a vanilla call and a cash digital

Draw the value of a vanilla call and of a digital (cash-or-nothing) call as functions of spot, and describe the relationship between them.

The digital is minus the strike derivative of the call. The vanilla is a convex curve rising from zero to roughly $S-Ke^{-rT}$; the digital is an S-shaped curve from $0$ up to $e^{-rT}$, steepest near the strike. A tight call spread, long $1/\varepsilon$ calls at $K-\varepsilon$ and short $1/\varepsilon$ at $K$, converges to the digital, so $D(K)=-\partial C/\partial K$.