There is not actually any need for remarking between the IP prec or TOS byte
The router just read different fields from the ToS byte in case of IPprec or DSCP.
The IP prec is just the first 3 high order bits of the TOS byte. The DSCP is the first 6 high order bits. You can read the next doc for detailed info
However, it is easier to have a common reference with your ISP regarding the QoS values to be eihter DSCP or IP Prec. Finally, pay attention if you use encryption over the ISP (e.g. IPsec or GRE.)
In this case, you have to use the relevant conf. to your edge router in order to have the correct QoS prioritization (qos pre classify command) over the ISP.
The default DSCP is 000 000. Class selector DSCPs are values that are backward compatible with IP precedence. When converting between IP precedence and DSCP, match the three most significant bits. In other words:
IP Prec 5 (101) maps to IP DSCP 101 000