This paper quantifies performance bounds of L1 adaptive controllers for linear uncertain systems with input quantization. Two basic types of quantizers are considered: uniform quantizers and logarithmic quantizers. The performance bounds of the L1 adaptive controller in the presence of input quantization proved to have an additional term, dependent upon the quality of quantization. The signals of the closed-loop L1 adaptive systems can be rendered arbitrarily close to the corresponding signals of a bounded reference system by increasing the adaptation rate and improving the quantizer. Simulations confirm the theoretical results.