Processor speed = \(4 \, \text{MHz} = 4 \times 10^6 \, \text{cycles per second}\).
DMA uses \(1\%\) of processor cycles, so the number of cycles used for DMA:
\[
{DMA cycles} = 1\% \times 4 \times 10^6 = 4 \times 10^4 \, \text{cycles per second}.
\]
Data transferred per DMA cycle = \(8 \, \text{bytes} = 8 \times 8 = 64 \, \text{bits}\).
Total data transfer rate:
\[
{Rate} = \text{DMA cycles} \times \text{Data per cycle} = 4 \times 10^4 \times 64 = 25,60,000 \, \text{bits per second}.
\]
Final Answer:
\[
\boxed{25,60,000 \, \text{bits per second}}
\]