The iterative circuit below compares two positive, unsigned

binary numbers X $=$ xn$1...$ x$1$x$0$ and Y $=$ yn$1...$ y$1$y$0.$ The numbers are

compared from right to left $($i$.$e$.,$ least significant bits to most significant bits$).$

$($a$)$ Derive the transition table for a typical cell, cell i$,$ so that anbn $=00$ if X $=$ Y$,$ anbn

$=01$ if X $>$ Y$,$ and anbn $=10$ if X $<$ Y$.$

$($b$)$ Derive minimum sum$-$of$-$product expressions for ai$+1$ and bi$+1.$