[14] compared 32-bit and 16-bit floating-point data formats without considering the impact of these in terms of hardware cost and additional data representation, such as fixed point. For exploring new custom co-processors, FPGAs are well-suitable platforms. In contrast to CPUs, GPUs, and DSPs that have a fixed instruction-set architecture (ISA) and data representations, FPGAs allow designers to define custom hardware architectures and to explore custom data representations [6]. Therefore, they can be used for exploring the design space, where different custom and standard data formats are defined and selected. **Contributions. ** In this article, we propose various hardware optimizations of the X-ray pre-processing step in interventional CT. It involves the optimization of the numerical computation of total attenuation values and its hardware acceleration. This pre-processing step is also called _10-correction_. First, we apply the pre-processing algorithm on the digital detector signals without the intermediate step to convert them to intensity images. Consequently, the total attenuation computation formula is simplified in terms of arithmetic and hardware complexity. Second, we implement a custom hardware accelerator as dataflow architecture, called the CT pre-processing core, that pre-processes the raw sensor data on the fly, without storing data in external memory. Furthermore, this core is designed using high-level synthesis (HLS), and it is configurable for various encoding and data widths of fixed-point and floating-point representations. In addition to the proposed pre-processing optimization, we integrated the implementation of the CT pre-processing core in an open-interface CT assembled in our laboratory. The proposed core implemented on FPGA can be integrated directly with the data acquisition system (DAS), which collects the detector signals and forwards the pre-processed data to the reconstruction system. Finally, we perform a design space exploration (DSE) to find which real number representation and data format better fits the pre-processing step for interventional CT applications. The DSE considers the different data representations as input variables and the qualitative and quantitative metrics, such as image quality, execution time, and the X-ray dose as decision variables. We systematically pre-select the input data formats based on the raw sensor and the reconstruction data formats. In addition, we pre-select specific metrics for estimating hardware costs, such as execution time, data width, and memory bandwidth required per pixel. Apart from that, we use image quality metrics, such as mean square error (MSE) of the 2D image and _low contrast_, _noise_ and _uniformity_ of the 3D volume. The image quality is analyzed after reconstructing the images of a dedicated CT image quality phantom known as CATPHAN(r) 500 [15] phantom [15]. **Structure. ** This paper is organized as follows: Section 2 describes the CT scanner, the difference between attenuation and intensity projection images, and the computing theory for real number representations; Section 3 explains the related works; Sections 4 and 5 present the optimization of projection pre-processing and the CT pre-processing core; Section 6 illustrates the implementation and the CT integration; Section 7 introduces the DSE for the different real number representations; Section 8 describes the phantom modules, the image quality metrics, and CT settings utilized for the DSE; Sections 9 and 10 show the results of the X-ray pre-processing for various real number representations.