Simple convertible bond question

When a convertible bond matures, is it a convention that you will not get the last coupon if you decide to convert the bond to shares? Example: conversion ratio is 8, coupon is 2%. At the maturity, I will get 1020 if I decide not to convert the bond to shares. If I decided to convert it, will I only get the 8 shares but not the $20 coupon? This is how it looks like on page 315, figure 32.5 in Advanced Core Topics. In the last period, the top three nodes do not include a coupon.

If you exercise your right to convert the bond to stock you loose any benefits associated with the bond. You don’t get anymore coupons and you don’t get a your principal back, you get the stock and any associated dividends. You can’t have both occurring at the same time. Hope that makes sense.