In the binary equation (1 p 101)₂+(10 ql )₂=(100 r 00)₂ where p , q and r are binary digits, what are the possible values of p, q and r respectively?

Step-by-step solution

aligned & (1 p 101)₂+(10 q 1)₂=(100 r 00)₂ & (1 2^4+ p 2^3+1 2^2+0 2^1+1 2^0 ) & + (1 2^3+0 2^2+ q 2^1+1 2^0 ) & =1 2^5+0+0+ r 2^2+0+0 aligned aligned & 16+8 p+4+1+8+2 q+1=32+4 r & 30+8 p+2 q=32+4 r & 8 p+2 q=2+4 r aligned from options, substitute p =0, q =1, r =0 we get 0+2(1)=2+0 2=2 .