The case of the register IChgTerm is much simpler to calculate. In order to achieve a value of 250mA (example in datasheet), we take the example hex value in the MAX17055 datasheet of 0x0640 and convert it to decimal, which is a value of 1600. We then multiply this value of 1600 by (01.5625 µV/RSENSE), which can be found in Table 1 of the datasheet in the "Current" row. RSENSE in this example is a10mΩ resistor. The register type can be found in the datasheet under the "IChgTerm" section. The product of 1600 and (01.5625 µV/RSENSE) gives you 250mA, which is the desired value.
For the Vempty the desired VR value is 3.3V while the desired VE value is 3.88V for a hex value of 0xA561. On page 12 in Table 2, it can be seen that VR is the most significant 9 bits while VE is the least significant 7 bits. To calculate each of these, you convert the hex value to binary, take the first 9 bits for VR and last 7 for VE, and convert those values to decimal. VR will come out to be 330 and VE will come out to be 97. In the datasheet on page 13 under the VR section, a 10mV resolution is mentioned, meaning you must multiply 330 by 10 mV, giving you the desired 3.3V value. The same goes for VE except the resolution is 40 mV, meaning we multiply 40 mV by 97 to get the desired 3.88V value.