  The Square Kilometre Array (SKA) is a planned multi purpose radio telescope
with a collecting area approaching 1 million square metres. One of the key
science objectives of the SKA is to provide exquisite strong-field tests of
gravitational physics by finding and timing pulsars in extreme binary systems
such as a pulsar-black hole binary. To find out how three preliminary SKA
configurations will affect a pulsar survey, we have simulated SKA pulsar
surveys for each configuration. We estimate that the total number of normal
pulsars the SKA will detect, using only the 1-km core and 30 minutes
integration time, is around 14000 normal pulsar and 6000 millisecond pulsars.
We describe a simple strategy for follow-up timing observations and find that,
depending on the configuration, it would take 1-6 days to obtain a single
timing point for 14000 pulsars. Obtaining a single timing point for the
high-precision timing projects of the SKA, will take less than 14 hours, 2
days, or 3 days, depending on the configuration. The presence of aperture
arrays will be of great benefit here. We also study the computational
requirements for beam forming and data analysis for a pulsar survey. Beam
forming of the full field of view of the single-pixel feed 15-m dishes using
the 1-km core of the SKA requires about 2.2*10^15 operations per second. The
corresponding data rate from such a pulsar survey is about 4.7*10^11 bytes per
second. The required computational power for a deep real time analysis is
estimated to be 1.2*10^16 operations per second. For an aperture array or
dishes equipped with phased array feeds, the survey can be performed faster,
but the computational requirements and data rates will go up.
