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;
- 4 026 531 829 ÷ 2 = 2 013 265 914 + 1;
- 2 013 265 914 ÷ 2 = 1 006 632 957 + 0;
- 1 006 632 957 ÷ 2 = 503 316 478 + 1;
- 503 316 478 ÷ 2 = 251 658 239 + 0;
- 251 658 239 ÷ 2 = 125 829 119 + 1;
- 125 829 119 ÷ 2 = 62 914 559 + 1;
- 62 914 559 ÷ 2 = 31 457 279 + 1;
- 31 457 279 ÷ 2 = 15 728 639 + 1;
- 15 728 639 ÷ 2 = 7 864 319 + 1;
- 7 864 319 ÷ 2 = 3 932 159 + 1;
- 3 932 159 ÷ 2 = 1 966 079 + 1;
- 1 966 079 ÷ 2 = 983 039 + 1;
- 983 039 ÷ 2 = 491 519 + 1;
- 491 519 ÷ 2 = 245 759 + 1;
- 245 759 ÷ 2 = 122 879 + 1;
- 122 879 ÷ 2 = 61 439 + 1;
- 61 439 ÷ 2 = 30 719 + 1;
- 30 719 ÷ 2 = 15 359 + 1;
- 15 359 ÷ 2 = 7 679 + 1;
- 7 679 ÷ 2 = 3 839 + 1;
- 3 839 ÷ 2 = 1 919 + 1;
- 1 919 ÷ 2 = 959 + 1;
- 959 ÷ 2 = 479 + 1;
- 479 ÷ 2 = 239 + 1;
- 239 ÷ 2 = 119 + 1;
- 119 ÷ 2 = 59 + 1;
- 59 ÷ 2 = 29 + 1;
- 29 ÷ 2 = 14 + 1;
- 14 ÷ 2 = 7 + 0;
- 7 ÷ 2 = 3 + 1;
- 3 ÷ 2 = 1 + 1;
- 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.
4 026 531 829(10) = 1110 1111 1111 1111 1111 1111 1111 0101(2)
3. 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) 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, 32,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 64.
4. 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.
Number 4 026 531 829(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:
4 026 531 829(10) = 0000 0000 0000 0000 0000 0000 0000 0000 1110 1111 1111 1111 1111 1111 1111 0101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.