Need help converting machine code
You've basically got the answer already: the s register is number 0b10001 = 17, the t register is number 0b10010 = 18.

The instruction is not quite the way you've said it: standard MIPS has the registers in the opposite order, so it's opcode rs rt immediate. The opcode is 0b001000 = 8 = ADDI; rs is 0b10001 = 17 = $s1; rt is 0b10010 = 18 = $s2; the immediate value is 0b0000000000001111 = 15.

(The prefix 0b indicates that the following number is in binary.)