using >>, -, + to make a number X times the constant K for the following numbers

Question

if were only allowed to use >>, -, + to make a number X times the constant K lets assume K is 17 and K is 20 how to make an expression for each

I was trying to think of ways to do this but I cant.

Answer 1

If $a$ is expressed in binary $$2^n\cdot a=a<<n$$ where $<<$ is the bitwise left shift operator.

$$17\cdot a=(2^4+1)\cdot a=(a<<4)+a$$ and $$20\cdot a=(2^4+2^2)\cdot a=(a<<4)+(a<<2)$$