propsitional logic statements and bits

Question

3 bit non negative integer x, and 4 bit non negative integer y. x is given by X2,X1,X0 and y is given by Y3,Y2,Y1,Y0. For any truth assignment t of these propositional variable ( 1 = true, 0 = false), x = 4t(x2)+2t(x1)+t(x0) and y = 8t(y3)+4t(y2)+2t(y1)+t(y0). Use logic connectives and propositional variables:X2,X1,X0 and Y3,Y2,Y1,Y0 to express propositional formula that is satisfied by truth assignment t for which y = x + 2

How do I start this question

Answer 1

You are being asked to express this addition in logical language. If $y=x+2$ the ones bits are the same, so $X0=Y0$ When you add $2$, you will change the twos bit, so $X1=1-Y1$ or maybe you want $X1=\lnot Y1$. That is a start. The fours bit is harder as you have to think about carries. The expression will involve the twos bits as well as the fours bits. Over to you.