In certain computer and communication systems, the significant number of byte errors are not hard errors, but a few transient bit errors confined to byte regions. This kind of byte errors are called spotty byte errors, meaning, not all, but only 2 or 3 random bits, are corrupted in a byte. Especially, the codewords of memory systems which use recent high density wide I/O data semiconductor DRAM chips are prone to this kind of spotty byte errors. This is because, the presence of strong electromagnetic waves in the environment or the bombardment of an energetic particle on a DRAM chip is highly likely to upset more than just one bit stored in that chip. Under this situation, codes capable of correcting single spotty byte errors are suitable for application in semiconductor memory systems. This paper defines a spotty byte error as a random t-bit error confined to a b-bit byte and proposes a class of codes called Single t/b-error Correcting (St/bEC) codes which are capable of correcting single spotty byte errors occurring in computer and communication systems. For the case where the chip data output is 16 bits, i.e., b=16, the S3/16EC code proposed in this paper requires only 16 check bits, that is, only one chip is required for check bits at practical information lengths such as 64, 128 and 256 bits. Furthermore, this S3/16EC code is capable of detecting more than 95% of all single 16-bit byte errors at information length 64 bits.