 Solution

A block code for line coding divides the data into five-bit groups and assigns each of the $2^5=32$ possible groups a distinct eight-bit codeword. The receiver reverses that assignment after finding the eight-bit boundaries. There are $2^8=256$ candidate codewords, so the designer has substantial freedom to select 32 suitable ones and reserve other patterns for control or synchronization.

The choice can limit long runs of equal bits to help clock recovery, balance high and low levels to reduce a persistent offset, and distinguish control patterns from data. These properties must hold across adjacent codeword boundaries too: two individually acceptable words can concatenate into an unacceptable run. The unused patterns can also help error detection and correction: an invalid received pattern exposes some errors, and the Hamming distance between valid codewords determines stronger guarantees. Redundancy alone does not imply that all errors are detected or correctable. Circuit complexity and propagation of a synchronization error also matter.

Before any further line coding or framing overhead, the useful fraction and expansion areThe three extra bits per five input bits are 60% overhead relative to the input, or 37.5% of the encoded output.