Does a digital ready tv needs a converter box?

No. If you already have a digital TV, when the digital transition occurs in February 2009, you will still receive broadcast signals from your antenna. There is no need to purchase additional equipment (a converter box).
If you do not already have a digital TV and you want to continue to receive broadcast signals from your antenna, then you will need to purchase a converter box to receive and translate those signals to your analogue television.
There is another choice that does not require the purchase of these new converter boxes: If you do not want to purchase additional equipment nor a new television because the one you have is "just fine" and as well you like the remote that came with the tv because you finally know where all the buttons are, then you can have installed as little as basic cable to all your TVs (no additional monthly cost for multiple basic or basic/standard cable TVs), get rid of the rabbit ears (antennas) altogether and enjoy clearer local channels and a few others you are sure to enjoy. The cost is surprisingly nominal, the set-up will be done for you, the ease of use exceptional.
Basic or basic/standard cable will enable you to turn on and off your tv the way you always have, use your own remote the way you are accustomed to use it. And if you ever need help, help is a phone call away, and in the case of TimeWarner cable, trouble service is free and usually local to your area.
If you would like more information about basic, basic/standard, Digital, Free High Definition or any other industry leading technologies and services, call your Local TimeWarner Cable office to request an in-home visit from a Direct Sales Representative who will provide you with the most thorough answers to your questions and as well the absolute best possible rates and discounts - apples to apples - in the market.