Answer:
[tex]-8375_{10} = -10001000011111_2[/tex]
[tex]-10001000011111_2 = -8735_{10[/tex]
Explanation:
Given
-8735
Required
Convert to binary and then back to decimal
To convert to binary, we divide by 2 and write down the remainder (ignore the negative sign, first)
8735 / 2 = 4367 R 1
4367 / 2 = 2183 R 1
2183 / 2 = 1091 R 1
1091 / 2 = 545 R 1
545 / 2 = 272 R 1
272 / 2 = 136 R 0
136 / 2 = 68 R 0
68 / 2 = 34 R 0
34 / 2 = 17 R 0
17 / 2 = 8 R 1
8 / 2 = 4 R 0
4 / 2 = 2 R 0
2 / 2 = 1 R 0
1 / 2 = 0 R 1
Write out the remainder from bottom to top
[tex]8735_{10} = 10001000011111_2[/tex]
Include the negative:
[tex]-8735_{10} = -10001000011111_2[/tex]
To convert to decimal, we simply multiply the individual digits with the base (in this case, it is base 2) raise to power of the index of that digit.
There are 14 digits in 10001000011111 and the rightmost digit is of index 0 and it increased to the left.
Ignore the negative, first; so, we have:
[tex]10001000011111_2 = 1 * 2^{13} + 0 * 2^{12} + 0 * 2^{11} + 0 * 2^{10} + 1 * 2^{9} + 0 * 2^{8} + 0 * 2^{7} + 0 * 2^{6} + 0 * 2^{5} + 1 * 2^{4} + 1 * 2^{3} + 1 * 2^{2} + 1* 2^{1} + 1 * 2^0[/tex]
[tex]10001000011111_2 = 1 * 8192 + 0 + 0 + 0 + 1 * 512 + 0 + 0 + 0 + 0 + 1 * 16 + 1 * 8 + 1 * 4 + 1* 2 + 1 * 1[/tex]
[tex]10001000011111_2 = 8192 + 512 + 16 + 8 + 4 + 2 + 1[/tex]
[tex]10001000011111_2 = 8735[/tex]
Include the negative sign
[tex]-10001000011111_2 = -8735_{10[/tex]
