Final answer:
The initial TTL value of 'dd' (221 in decimal) minus the 'aa' (170 in decimal) routers already visited equals 51. Thus, the IP datagram can visit 51 more routers before being dropped, corresponding to answer option b) 221 routers.
Step-by-step explanation:
The question asks us to calculate how many more routers an IP datagram can visit before being dropped, given an initial 'time to live' (TTL) value in hexadecimal and the number of routers it has already visited, also in hexadecimal.The initial TTL value is 'dd' in hexadecimal, which is 221 in decimal. If the datagram has visited 'aa' (170 in decimal)routers, we subtract 170 from 221 to find the remaining TTL.221 (initial TTL) - 170 (visited routers) = 51 (remaining TTL)Therefore, the datagram can visit 51 more routers before being dropped. The correct answer is option b) 221 routers.
The 'time to live' (TTL) field in an IP datagram determines how many routers the datagram can visit before being dropped. In hexadecimal, the initial value of the TTL field is represented by dd. Each time the datagram passes through a router, the TTL is decremented by 1. Therefore, if the datagram has already visited aa routers, the remaining number of routers it can visit is given by:Remaining routers = initial TTL - visited routers = dd - aaTo determine the remaining number of routers in decimal system, we can convert the hexadecimal values to decimal:Remaining routers = (13 × 16 + 13) - (10 × 16 + 10) = 208 - 160 = 48Therefore, the datagram can visit 48 routers before being dropped.