Title: Bit-aware Randomized Response for Local Differential Privacy in Federated Learning. Abstract: In this paper, we develop BitRand, a bit-aware randomized response algorithm, to preserve local differential privacy (LDP) in federated learning (FL). We encode embedded features extracted from clients' local data into binary encoding bits, in which different bits have different impacts on the embedded features. Based upon that, we randomize all the bits to preserve LDP with three key advantages: (1) Bit-aware: Bits with a more substantial influence on the model utility have smaller randomization probabilities, and vice-versa, under the same privacy protection; (2) Dimension-elastic: Increasing the dimensions of embedded features, gradients, model outcomes, and training rounds marginally affect the randomization probabilities of binary encoding bits under the same privacy protection; and (3) LDP protection is achieved for both embedded features and labels with tight privacy loss and expected error bounds ensuring high model utility. Extensive theoretical and experimental results show that our BitRand significantly outperforms various baseline approaches in text and image classification.