issues with sampling rate in Giga Hertz : array exceeds maximum array size preference array exceeds maximum array size preference.

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I would like to model a unit step function of a digital system with sampling clock running at 1 GHz. My undertanding is sampling rate in matlab is specified in Hertz. So, for 1 GHz sampling rate if I exceute the below,, I get the message and matlab is unresponsive . How can I model a 1GHz system sampling rate (or) can I accomplish the sane with Fs=1 Hz and still accurately model the digital system running at 1 GHz clock?
Fs = 1000000000; %sampling rate in hertz ( 10 power 9 = Giga Hertz)
Ts = 1/Fs; %sampling time interval in seconds
t = 0:Ts:1000-Ts; %sampling period
unitstep = t>=1;
plot (t, unitstep);
Requested 1000000000000x1 (7450.6GB) array exceeds maximum array size preference array exceeds maximum array size preference. Creation of arrays greater than this limit may take a long time and cause MATLAB to become unresponsive. See array size limit or preference panel for more information.

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