So in mastering bitcoin it mentioned that to generate child key,The left-half 256 bits of the hash are added to the parent key so if we add that it will be 512 bits.But we need 256 bit so do we hash that string (parent key + left hash) with SHA256 and get the 256 bit child private key?
There is concatenation where 256 bits placed next to another 256 bits makes 512 bits. However, what you are referring to (generating a child key) uses scalar addition. A 256 bit number (256 bit parent private key) is added to another 256 bit number (left 256 bits of the SHA512) and the result modulo p (
p = 2^256-2^32-977) is another 256 bit number.