The increasing size of large neural network models, specifically language models and foundational image models, poses deployment challenges, prompting efforts to reduce memory requirements and enhance computational efficiency. These efforts are critical to ensure practical deployment and effective utilization of these models across various applications. In this work, a novel type of neural network layers and models is developed that uses only single-bit parameters. In this novel type of models all parameters of all layers, including kernel weights and biases, only have values equal to zero or one. This novel type of models uses layers named as binary normalized layer. These binary normalized layers can be of any type, such as fully connected, convolutional, attention, etc., and they consist of slight variations of the corresponding conventional layers. To show the effectiveness of the binary normalized layers, two different models are configured to solve a multiclass image classification problem and a language decoder to predict the next token of a sequence. The model to solve the image classification has convolutional and fully connected layers, and the language model is composed of transformer blocks with multi-head attention. The results show that models with binary normalized layers present almost the same results obtained by equivalent models with real 32-bit parameters. The binary normalized layers allow to develop models that use 32 times less memory than current models and have equivalent performance. Besides, the binary normalized layers can be easily implemented on current computers using 1-bit arrays, and do not require the development of dedicated electronic hardware. This novel type of layers opens a new era for large neural network models with reduced memory requirements that can be deployed using simple and cheap hardware, such as mobile devices or only cpus.