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;
- 1 140 700 575 ÷ 2 = 570 350 287 + 1;
- 570 350 287 ÷ 2 = 285 175 143 + 1;
- 285 175 143 ÷ 2 = 142 587 571 + 1;
- 142 587 571 ÷ 2 = 71 293 785 + 1;
- 71 293 785 ÷ 2 = 35 646 892 + 1;
- 35 646 892 ÷ 2 = 17 823 446 + 0;
- 17 823 446 ÷ 2 = 8 911 723 + 0;
- 8 911 723 ÷ 2 = 4 455 861 + 1;
- 4 455 861 ÷ 2 = 2 227 930 + 1;
- 2 227 930 ÷ 2 = 1 113 965 + 0;
- 1 113 965 ÷ 2 = 556 982 + 1;
- 556 982 ÷ 2 = 278 491 + 0;
- 278 491 ÷ 2 = 139 245 + 1;
- 139 245 ÷ 2 = 69 622 + 1;
- 69 622 ÷ 2 = 34 811 + 0;
- 34 811 ÷ 2 = 17 405 + 1;
- 17 405 ÷ 2 = 8 702 + 1;
- 8 702 ÷ 2 = 4 351 + 0;
- 4 351 ÷ 2 = 2 175 + 1;
- 2 175 ÷ 2 = 1 087 + 1;
- 1 087 ÷ 2 = 543 + 1;
- 543 ÷ 2 = 271 + 1;
- 271 ÷ 2 = 135 + 1;
- 135 ÷ 2 = 67 + 1;
- 67 ÷ 2 = 33 + 1;
- 33 ÷ 2 = 16 + 1;
- 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.
1 140 700 575(10) = 100 0011 1111 1101 1011 0101 1001 1111(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) indicates 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.
1 140 700 575(10) = 0100 0011 1111 1101 1011 0101 1001 1111
6. Get the negative integer number representation:
To write the negative integer number on 32 bits (4 Bytes),
as a signed binary in one's complement representation,
... replace all the bits on 0 with 1s and all the bits set on 1 with 0s.
Reverse the digits, flip the digits:
Replace the bits set on 0 with 1s and the bits set on 1 with 0s.
-1 140 700 575(10) = !(0100 0011 1111 1101 1011 0101 1001 1111)
Number -1 140 700 575(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in one's complement representation:
-1 140 700 575(10) = 1011 1100 0000 0010 0100 1010 0110 0000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.