Definition of 'taxable supply' and 'aggregate turnover'

As per definitions given in CGST Act, 2017, 'taxable supply' would mean supply which are leviable to tax under the Act. Would this mean that exempt supplies and zero rated supplies would also become 'taxable supply' as tax is to be levied on them but they are exempted by notification or because their tax rate is 0?
If this is the case, why does the term 'aggregate turnover' mentions that along with 'taxable supplies' one must also add 'exempted supplies'? Wouldn't taxable supplied include exempted supplies?
Also, in the case of suppliers who have applied for composition schemes and who are not manufacturers or restraunt service providers, the rate of tax shall be applied on 'taxable supplies of goods and services'. As the definition of 'taxable supply' means supply leviable to tax and exempted goods are in fact leviable to tax, would this mean while computing the tax liability of a supplier opting to pay tax under the composition scheme, we must also compute tax on his exempted supplies?