## 3 Development of the Proposed Computational Unit
### Application of the Proposed Computational Unit for Medical Image Compression  
This research considers a medical image, a CT scan of the brain for aneurysm detection of size 512 \(\times\) 512 taken from the open-access database of medical images [35]. Block style of DCT coding is followed in the DCT approach, in which the DCT is applied over blocks of a fixed size of 8 \(\times\) 8. So, for an image of size 512 \(\times\) 512, there are 4096 blocks to which DCT is applied to get the DCT of the entire image. The structure of the encoding of the digital image compression referred to in this research work is depicted in Figure 12.  
The compression ratios can be improvised by replacing the gray code with the binary code when the original digital image is represented and utilized in the image compression process [36]. A considerable improvement in the compression ratio was observed in this research work by utilizing gray code [37]. The original image in binary code is first converted to gray code using a binary-to-gray code converter. Gray coding offers a vibrant property of requiring a single bit change from a value \"G\" to \"G + 1\" or \"G - 1\" unlike binary codes, making gray coding an attractive addition to applications demanding lesser power consumption. Figure 13 illustrates the transitioning of bits for both gray and binary codes from numbers 0 to 15. Figure 12: Encoding block of DCT Image Compression. Figure 13: Bit Transitioning for Binary and Gray Codes. The image is then divided into 8 \(\times\) 8 blocks, to which DCT is applied. Several fast DCT algorithms have been proposed recently for the practical computation of image compression. Most of the proposed algorithms were focused on minimizing the addition and multiplication operations associated with the butterfly blocks incorporated in the DCT algorithms. The algorithm proposed by [PERSON] proved to be the fastest, with just 11 multiplications and 29 additions, making it the ideal choice for this research work [38]. The structure of the 8-point DCT structure incorporating the computational unit in [PERSON]'s algorithm is illustrated in Figure 14. The adders used for computations in the butterfly diagram are replaced by the ET adders by incorporating the computational unit designed in this research work, reducing the power. The multiplications involved are reduced by approximating the cosine constants as given in Table 3 to one wherever applicable, and in cases where multiplications were required, it was achieved using the low-power multipliers and shifters, as illustrated in Figure 14.  
The bit-width of the digital input images is 10 bits, and after the row DCT, the output images' bit-width is 14 bits. The second column DCT and first row IDCT had an input and output bit-width of 14 bits. Finally, 14 was the bit-width of the last column IDCT, with the output image having a bit-width of 10 bits. The next step is quantization, where the high-frequency DCT coefficients that are not imperative are reduced to 0. The quantization process is achieved by dividing each 8 \(\times\) 8 block by a coefficient Q (u,v) obtained using the quantization matrix. As the division involved is an integer computation, most coefficients are 0, whereas the remaining coefficients are smaller numbers. A situation ideal for run length encoding and entropy encoding is obtained now. The quantization matrix determines the quality of the compression. Figure 14: An 8-point Loeffler’s DCT flow diagram incorporating the computational unit. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**a** & **b** & **c** & **d** & **e** & **f** & **g** & **h** \\ \hline \(sin\frac{\pi}{16}\) & \(cos\frac{\pi}{16}\) & \(sin\frac{3\pi  
Larger values in the quantization table are chosen for lower quality, resulting in higher compression rates. \[Q(u,v)=