1. Start with the positive version of the number:
|-2 149 999 941| = 2 149 999 941
2. Divide the number repeatedly by 2:
Keep track of each remainder.
We stop when we get a quotient that is equal to zero.
- division = quotient + remainder;
- 2 149 999 941 ÷ 2 = 1 074 999 970 + 1;
- 1 074 999 970 ÷ 2 = 537 499 985 + 0;
- 537 499 985 ÷ 2 = 268 749 992 + 1;
- 268 749 992 ÷ 2 = 134 374 996 + 0;
- 134 374 996 ÷ 2 = 67 187 498 + 0;
- 67 187 498 ÷ 2 = 33 593 749 + 0;
- 33 593 749 ÷ 2 = 16 796 874 + 1;
- 16 796 874 ÷ 2 = 8 398 437 + 0;
- 8 398 437 ÷ 2 = 4 199 218 + 1;
- 4 199 218 ÷ 2 = 2 099 609 + 0;
- 2 099 609 ÷ 2 = 1 049 804 + 1;
- 1 049 804 ÷ 2 = 524 902 + 0;
- 524 902 ÷ 2 = 262 451 + 0;
- 262 451 ÷ 2 = 131 225 + 1;
- 131 225 ÷ 2 = 65 612 + 1;
- 65 612 ÷ 2 = 32 806 + 0;
- 32 806 ÷ 2 = 16 403 + 0;
- 16 403 ÷ 2 = 8 201 + 1;
- 8 201 ÷ 2 = 4 100 + 1;
- 4 100 ÷ 2 = 2 050 + 0;
- 2 050 ÷ 2 = 1 025 + 0;
- 1 025 ÷ 2 = 512 + 1;
- 512 ÷ 2 = 256 + 0;
- 256 ÷ 2 = 128 + 0;
- 128 ÷ 2 = 64 + 0;
- 64 ÷ 2 = 32 + 0;
- 32 ÷ 2 = 16 + 0;
- 16 ÷ 2 = 8 + 0;
- 8 ÷ 2 = 4 + 0;
- 4 ÷ 2 = 2 + 0;
- 2 ÷ 2 = 1 + 0;
- 1 ÷ 2 = 0 + 1;
3. Construct the base 2 representation of the positive number:
Take all the remainders starting from the bottom of the list constructed above.
2 149 999 941(10) = 1000 0000 0010 0110 0110 0101 0100 0101(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 32.
A signed binary's bit length must be equal to a power of 2, as of:
21 = 2; 22 = 4; 23 = 8; 24 = 16; 25 = 32; 26 = 64; ...
The first bit (the leftmost) is reserved for the sign:
0 = positive integer number, 1 = negative integer number
The least number that is:
1) a power of 2
2) and is larger than the actual length, 32,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 64.
5. Get the positive binary computer representation on 64 bits (8 Bytes):
If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 64:
2 149 999 941(10) = 0000 0000 0000 0000 0000 0000 0000 0000 1000 0000 0010 0110 0110 0101 0100 0101
6. Get the negative integer number representation:
To get the negative integer number representation on 64 bits (8 Bytes),
... change the first bit (the leftmost), from 0 to 1...
Number -2 149 999 941(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-2 149 999 941(10) = 1000 0000 0000 0000 0000 0000 0000 0000 1000 0000 0010 0110 0110 0101 0100 0101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.