Denominator of crude death rate is -
Crude death rate

It is the simplest measure of mortality.
It is defined as "the number of death (from all causes) per 1000 estimated mid-year population in one year, in a given place".

Crude death rate = No. of death during the year / Mid-year population x 1000
Specific death rates 

When analysis is planned to throw light on etiology, it is essential to use specific death rates.
The specified death rate helps identify particular 'at risk' group (s) for prevention.
It also permits comparison between different causes within same population.
The specific death rates may be -


Cause or disease specific, e.g. TB, cancer, accident.
Related to specific groups - e.g. age specific, sex specific.

Examples -
Specific death rate due to TB = No. of deaths due to TB in year / Mid year population x 1000
Specific death rate for male = No. of deaths amongst males / Mid year population of males x 1000
1000 live birth
Mid year population
Total number of deaths in a community
Total number of case population in community