 Digital comparator

A combinational logic device comparing two fixed-width binary representations. For unsigned inputs $a,b$, a two-output encoding is $L=1$ exactly when $a<b$ and $G=1$ exactly when $a>b$. Equality gives $(L,G)=(0,0)$; $(1,1)$ is unreachable. A one-bit implementation is $L=\neg a\wedge b$, $G=a\wedge \neg b$.