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;
- 1 140 850 688 ÷ 2 = 570 425 344 + 0;
- 570 425 344 ÷ 2 = 285 212 672 + 0;
- 285 212 672 ÷ 2 = 142 606 336 + 0;
- 142 606 336 ÷ 2 = 71 303 168 + 0;
- 71 303 168 ÷ 2 = 35 651 584 + 0;
- 35 651 584 ÷ 2 = 17 825 792 + 0;
- 17 825 792 ÷ 2 = 8 912 896 + 0;
- 8 912 896 ÷ 2 = 4 456 448 + 0;
- 4 456 448 ÷ 2 = 2 228 224 + 0;
- 2 228 224 ÷ 2 = 1 114 112 + 0;
- 1 114 112 ÷ 2 = 557 056 + 0;
- 557 056 ÷ 2 = 278 528 + 0;
- 278 528 ÷ 2 = 139 264 + 0;
- 139 264 ÷ 2 = 69 632 + 0;
- 69 632 ÷ 2 = 34 816 + 0;
- 34 816 ÷ 2 = 17 408 + 0;
- 17 408 ÷ 2 = 8 704 + 0;
- 8 704 ÷ 2 = 4 352 + 0;
- 4 352 ÷ 2 = 2 176 + 0;
- 2 176 ÷ 2 = 1 088 + 0;
- 1 088 ÷ 2 = 544 + 0;
- 544 ÷ 2 = 272 + 0;
- 272 ÷ 2 = 136 + 0;
- 136 ÷ 2 = 68 + 0;
- 68 ÷ 2 = 34 + 0;
- 34 ÷ 2 = 17 + 0;
- 17 ÷ 2 = 8 + 1;
- 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.
1 140 850 688(10) = 100 0100 0000 0000 0000 0000 0000 0000(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 31.
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, 31,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 32.
5. Get the positive binary computer representation on 32 bits (4 Bytes):
If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 32:
1 140 850 688(10) = 0100 0100 0000 0000 0000 0000 0000 0000
6. Get the negative integer number representation:
To get the negative integer number representation on 32 bits (4 Bytes),
... change the first bit (the leftmost), from 0 to 1...
Number -1 140 850 688(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-1 140 850 688(10) = 1100 0100 0000 0000 0000 0000 0000 0000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.