To which physical address $($in binary format$)$ does the logical address $0011011010101010$ correspond, under the following hypothetical memory management schemes? Justify your answers.

a$)$A paging system with a page table containing $512$ entries and in which the frame number happens to be two times larger than the page number.

b$)$A segmentation system with a maximum segment size of $2,048$ bytes, using a segment table in which bases happen to be regularly placed at real addresses equal to $22+4,096+$ segment number.