Sure, let’s convert the decimal number (2536475891_{10}) to binary and hexadecimal.
Binary Conversion:
To convert (2536475891_{10}) to binary, we repeatedly divide by 2 and note down the remainders until the quotient becomes 0.
[
\begin{align} 2536475891_{10} &= 2 \times 1268237945 + 1 \quad (\text{remainder}) \ 1268237945 &= 2 \times 634118972 + 1 \quad (\text{remainder}) \ 634118972 &= 2 \times 317059486 + 0 \quad (\text{remainder}) \ 317059486 &= 2 \times 158529743 + 0 \quad (\text{remainder}) \ 158529743 &= 2 \times 79264871 + 1 \quad (\text{remainder}) \ 79264871 &= 2 \times 39632435 + 1 \quad (\text{remainder}) \ 39632435 &= 2 \times 19816217 + 1 \quad (\text{remainder}) \ 19816217 &= 2 \times 9908108 + 1 \quad (\text{remainder}) \ 9908108 &= 2 \times 4954054 + 0 \quad (\text{remainder}) \ 4954054 &= 2 \times 2477027 + 0 \quad (\text{remainder}) \ 2477027 &= 2 \times 1238513 + 1 \quad (\text{remainder}) \ 1238513 &= 2 \times 619256 + 1 \quad (\text{remainder}) \ 619256 &= 2 \times 309628 + 0 \quad (\text{remainder}) \ 309628 &= 2 \times 154814 + 0 \quad (\text{remainder}) \ 154814 &= 2 \times 77407 + 0 \quad (\text{remainder}) \ 77407 &= 2 \times 38703 + 1 \quad (\text{remainder}) \ 38703 &= 2 \times 19351 + 1 \quad (\text{remainder}) \ 19351 &= 2 \times 9675 + 1 \quad (\text{remainder}) \ 9675 &= 2 \times 4837 + 1 \quad (\text{remainder}) \ 4837 &= 2 \times 2418 + 1 \quad (\text{remainder}) \ 2418 &= 2 \times 1209 + 0 \quad (\text{remainder}) \ 1209 &= 2 \times 604 + 1 \quad (\text{remainder}) \ 604 &= 2 \times 302 + 0 \quad (\text{remainder}) \ 302 &= 2 \times 151 + 0 \quad (\text{remainder}) \ 151 &= 2 \times 75 + 1 \quad (\text{remainder}) \ 75 &= 2 \times 37 + 1 \quad (\text{remainder}) \ 37 &= 2 \times 18 + 1 \quad (\text{remainder}) \ 18 &= 2 \times 9 + 0 \quad (\text{remainder}) \ 9 &= 2 \times 4 + 1 \quad (\text{remainder}) \ 4 &= 2 \times 2 + 0 \quad (\text{remainder}) \ 2 &= 2 \times 1 + 0 \quad (\text{remainder}) \ 1 &= 2 \times 0 + 1 \quad (\text{remainder}) \ 0 &= \text{end of division} \end{align}
]
Now, reading the remainders from bottom to top, we get:
[2536475891_{10} = 1001011111100111010110111010011_{2}]
Hexadecimal Conversion:
To convert (2536475891_{10}) to hexadecimal, we can convert the binary representation we obtained earlier to hexadecimal. Grouping the binary digits into groups of 4 from the right, we get:
[1001 \quad 0111 \quad 1110 \quad 0111 \quad 0101 \quad 1011 \quad 1010 \quad 0011_{2}]
Converting each group of 4 binary digits to their respective hexadecimal equivalents:
[1001_2 = 9_{16},]
[0111_2 = 7_{16},]
[1110_2 = E_{16},]
[0111_2 = 7_{16},]
[0101_2 = 5_{16},]
[1011_2 = B_{16},]
[1010_2 = A_{16},]
[0011_2 = 3_{16}.]
So, the hexadecimal representation of (2536475891_{10}) is (97E755BA3_{16}).