Unfortunately you have not told us what it is calculating for each code set up so we can help you.  From what you have said, your books items have HST Tax Exempt set to Yes but GST Tax Exempt set to No, your services have GST Tax Exempt set to Yes and HST set to No on the Taxes tab of each item.  Is this correct?

You have set up a default sales tax code for each supplier and client on the Taxes tab of each supplier/client ledger but left the Tax Exempt status unchanged at No for each tax.  Is this correct?

When you open the sales or purchases module, don't pick a client or supplier, enter $100 for the amount on the first line and an account.  Then pick a tax code.  What does the journal entry look like from the Reports menu?

Bear in mind that you cannot

C.Stewart said:

I have entered specific tax codes for each INVENTORY  item ie. GST only on books and HST only on services.

because you cannot set tax codes for items, you can only set whether they are tax exempt or not.