You have to use equipment called CHN Analyzer to determine the carbon fraction or percentage in selected sample amount then you can calculate for full biomass (multiplying with total mass of biomass).
According to Su-Hwa Jung, also is possible through thermal analyzer (ASTM E1131) in one run switching between inert (N2, He, or Ar) or oxidant atmosphere (air, O2).
An alternative method to ASTM, to determine the proximate analysis of biomass, is thermogravimetric analysis. Here is a recent publication that discusses the methodology using TGA.
Article Biomass proximate analysis using thermogravimetry
Fixed Carbon (ASTM E870): Solid, combustible residue that is the final calculation of the amount present in a biomass sample after the percentages of moisture, ash, and volatile matter have been determined.
First you measure Moisture content, then volatile matter, and finally burn the sample to find ash. The fixed carbon is so:
Fixed carbon is not total carbon. Total carbon can be measured with an elemental analyser, but fixed carbon is the amount you get after having pyrolysed the biomass is specific conditions. So it is important to follow a standard (e.g. ASTM) method such as those which have been suggested, as the carbon yield is very dependent on the heating rate. Therefore, your data can be compared with others only if obtained in the same conditions.
Is it supposed to apply the determination of moisture, volatiles and ashes/fixed carbon in sequence starting from an initial sample mass of 1 g, right?
The means that the ash, moisture, fixed carbon and volatile matters must measured and therefore to get one of them from calculation, measure the others.