1. 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;
- 1 207 959 570 ÷ 2 = 603 979 785 + 0;
- 603 979 785 ÷ 2 = 301 989 892 + 1;
- 301 989 892 ÷ 2 = 150 994 946 + 0;
- 150 994 946 ÷ 2 = 75 497 473 + 0;
- 75 497 473 ÷ 2 = 37 748 736 + 1;
- 37 748 736 ÷ 2 = 18 874 368 + 0;
- 18 874 368 ÷ 2 = 9 437 184 + 0;
- 9 437 184 ÷ 2 = 4 718 592 + 0;
- 4 718 592 ÷ 2 = 2 359 296 + 0;
- 2 359 296 ÷ 2 = 1 179 648 + 0;
- 1 179 648 ÷ 2 = 589 824 + 0;
- 589 824 ÷ 2 = 294 912 + 0;
- 294 912 ÷ 2 = 147 456 + 0;
- 147 456 ÷ 2 = 73 728 + 0;
- 73 728 ÷ 2 = 36 864 + 0;
- 36 864 ÷ 2 = 18 432 + 0;
- 18 432 ÷ 2 = 9 216 + 0;
- 9 216 ÷ 2 = 4 608 + 0;
- 4 608 ÷ 2 = 2 304 + 0;
- 2 304 ÷ 2 = 1 152 + 0;
- 1 152 ÷ 2 = 576 + 0;
- 576 ÷ 2 = 288 + 0;
- 288 ÷ 2 = 144 + 0;
- 144 ÷ 2 = 72 + 0;
- 72 ÷ 2 = 36 + 0;
- 36 ÷ 2 = 18 + 0;
- 18 ÷ 2 = 9 + 0;
- 9 ÷ 2 = 4 + 1;
- 4 ÷ 2 = 2 + 0;
- 2 ÷ 2 = 1 + 0;
- 1 ÷ 2 = 0 + 1;
2. Construct the base 2 representation of the positive number:
Take all the remainders starting from the bottom of the list constructed above.
1 207 959 570(10) = 100 1000 0000 0000 0000 0000 0001 0010(2)
3. 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.
4. 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.
Number 1 207 959 570(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in two's complement representation:
1 207 959 570(10) = 0100 1000 0000 0000 0000 0000 0001 0010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.