Total number of binary string of length $10$ is $2^{10} =1024$ as each position has $2$ options - $0$ or $1.$
Number of binary string of length $10$ and ending with $111 = 2^7 = 128$ (last $3$ positions being fixed)
$\therefore$ The number of binary string not ending with $111 = 1024-128 = 896.$