Comparator

Hardware Components that allow for comparing if a input vector is larger than another.

Basic Comparators

• 1-Bit Comparator
• 2-Bit Comparator

General Comparator

$A==B$

For $n$ bit digits: $A==B=A_1\ast B_1+{\overline{A}}_1\ast {\overline{B}}_1+\cdots +A_n\ast B_n+{\overline{A}}_n\ast {\overline{B}}_n$

$A>B$

$A>B=A_n\ast {\overline{B}}_n+(A_n\ast B_n+{\overline{A}}_n\ast {\overline{B}}_n)\ast A_{n-1}\ast {\overline{B}}_{n-1}+\cdots +A_0\ast {\overline{B}}_0\ast {\pi }_{k=1}^n(A_k\ast B_k+{\overline{A}}_k\ast {\overline{B}}_k)$

$A<B$

$A<B={\overline{A}}_n\ast B_n+(A_n\ast B_n+{\overline{A}}_n\ast {\overline{B}}_n)\ast {\overline{A}}_{n-1}\ast B_{n-1}+\cdots +{\overline{A}}_0\ast B_0\ast {\pi }_{k=1}^n(A_k\ast B_k+{\overline{A}}_k\ast {\overline{B}}_k)$