Of course, dietary sugar can raise your blood sugar, but something else can do it too. In fact, it's pretty significant. It's called gluconeogenesis. 
Gluconeogenesis means that your body is generating new glucose from non-carbohydrate sources. Your body can make new sugar from fat or protein. High blood sugar is not just about dietary sugar. Your body makes sugar from other things. 
The amount of sugar in your blood is significantly coming from gluconeogenesis. Diabetics have enhanced gluconeogenesis. So, your liver and your kidneys are making a lot of sugar, which raises your blood sugar. 
It's important to keep in mind that the body doesn't need much sugar. There are very few parts of the body that are dependent on sugar. Everything else can live on other sources of fuel, like fatty acid and ketones. 
The body has the ability to make the sugar that it needs. We don't need to get sugar or carbohydrates from the diet. However, we do need dietary fiber, which is considered a carbohydrate. 
If you're a diabetic, your body is making too much sugar because insulin isn't working correctly in your body. Even though there might be high levels of insulin in the blood, the insulin is dysfunctional because of insulin resistance. Insulin isn't doing its job, which is to keep gluconeogenesis in check. 
The real problem is insulin resistance. This is what's causing the high levels of sugar in your blood. I believe the best thing to do would be to focus on fixing your insulin resistance. This could potentially help your body make less sugar and improve your blood sugar levels. In my opinion, the best way to improve insulin resistance is to do the Healthy Keto diet and intermittent fasting. 
What if you've already started the ketogenic diet and intermittent fasting, and you're seeing improvements, but you still have high blood sugar? Your body is likely still in the process of dealing with your insulin resistance. It takes time to reverse insulin resistance. The key is to not give up, stay consistent, and know what's really going on. 

Dr. Eric Berg DC Bio:
Dr. Berg, 51 years of age is a chiropractor who specializes in weight loss through nutritional & natural methods. His private practice is located in Alexandria, Virginia. His clients include senior officials in the U.S. government & the Justice Department, ambassadors, medical doctors, high-level executives of prominent corporations, scientists, engineers, professors, and other clients from all walks of life. He is the author of The 7 Principles of Fat Burning.
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