My left big toe stays purple most of the time. do i have diabetes?

No: That is not a typical sign for diabetes, but you should get evaluated by your pcp.

See your doctor: The toe is a separate issue from your possible diabetes. Your doctor can ask some questions, examine you, check a blood sample and tell you if you're diabetic. Your purple toe could be a sign of peripheral artery disease (pad), which is best managed by a vascular surgeon.

Many possibilities: Discoloration of the toe can be due to trauma, infection or a vascular compromise.