The difference between half and full duplex is the ability to receive and send sound at the same time. This is important for something like a phone conversation because with half duplex only one person can speak at a time and the other can't be heard until the other person completely stops talking. Knowing what your sound card can do is important if you want to use it for chatting online or playing and recording sound at the same time.
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Check the paperwork. This is always the first thing to check. Look at the box if you still have it. Next, check the manual and the website for the sound card. Look under the product area, choose your card and look for specifications. The information may not be listed but it's the first place you should look.
Install and run diagnostic software. One example is a program called Belarc Advisor. Once you run this type of software, it will generate a list of all of your computer's hardware with a lot of the specifications.
Try playing something and recording something at the same time. This is the ultimate test that will let you know for sure. Play something such as a Windows computer sound file, MP3 or other audio on your computer. Connect a microphone to the sound card and open a program such as Audacity and record something while the sound is playing. If you can do both at the same time, your card is full duplex.