Final answer:
To calculate the number of address bits for a 1GB memory with 4 bytes per word, divide the memory size by the word size to get 268,435,456 addressable locations, requiring 28 address bits. The address decoder would need to accommodate these 28 bits to uniquely identify each memory location.
Step-by-step explanation:
To determine address bits and an address decoder for a 1GB memory size with 4 bytes per word, you need to understand the memory addressing concept. The total number of addressable locations in memory is the memory size divided by the word size. In this case, 1GB equals 1,073,741,824 bytes. Therefore, the total addressable locations are 1,073,741,824 bytes / 4 bytes = 268,435,456 words.
Each location is uniquely identified by a binary address. The number of address bits needed is log2 of the number of addresses. Therefore, address bits = log2(268,435,456) = 28 bits.
An address decoder is designed to select a specific memory location based on the address provided. A decoder with 28 bits can uniquely decode the 268,435,456 addresses required for 1GB memory organized as 4 bytes per word.