Fully Homomorphic Encryption (FHE) allows computations on encrypted data without requiring access to the secret key. Existing FHE schemes are based on lattice cryptography and encode ciphertexts with a noise term necessary for security. However, this noise grows with each homomorphic operation, and once it exceeds a certain threshold, decryption fails. This imposes a limit on the complexity of computations that can be performed. Bootstrapping is a technique that overcomes this limitation by homomorphically evaluating the decryption function of the FHE scheme itself, effectively "refreshing" the ciphertext. After bootstrapping, the noise depends only on the complexity of evaluating the decryption function and not on the input ciphertext's noise. For efficiency, it is crucial to keep this added noise as low as possible. A central part of the decryption, and the main contributor to noise growth, is a rounding operation. In FHE, this is implemented by using digit extraction polynomials to extract least significant digits and then subtracting them. In this thesis, we focus on the digit extraction step of bootstrapping. We provide a practical method for constructing suitable polynomials, using Newton interpolation adapted to modular arithmetic. Our approach aims to find polynomials that minimize the resulting noise growth. We analyse the noise growth theoretically by deriving asymptotic upper bounds based on prior work, and we validate these findings empirically by implementing the digit extraction algorithms using the Microsoft SEAL homomorphic encryption library. Our evaluation compares the digit extraction methods across different parameters in terms of noise size, and performance.