Bandwidth required to transmit a binary sequence
It's not meaningful, in my opinion, to talk of the "bandwidth" of a constant number.  Unless you want to characterize that constant number as DC (because the value does not change in time).  And the bandwidth of DC is zero.

But a stream of bits toggling on and off, yes, a bandwidth (which is the rate of change of the bits or "bitrate", if we're considering two-sided bandwidth or half the bitrate if we're considering the single-sided bandwidth) is meaningful.

In fact, a very important fundamental theorem from Claude Shannon relates bandwidth, signal-to-noise ratio, and rate of information together.