The aim of this paper is to characterize the uniform exponential dichotomy of semigroups of linear operators in terms of the solvability of discrete-time equations over $N$. We give necessary and sufficient conditions for uniform exponential dichotomy of a semigroup on a Banach space $X$ in terms of the admissibility of the pair $(l^\infty(N, X), c_{00}(N,X))$. As an application we deduce that a $C_0$-semigroup is uniformly exponentially stable if and only if the pair $(C_b(R_+, X), C_{00}(R_+, X))$ is admissible for it and a certain subspace is closed and complemented in $X$.