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;
- 10 101 011 013 ÷ 2 = 5 050 505 506 + 1;
- 5 050 505 506 ÷ 2 = 2 525 252 753 + 0;
- 2 525 252 753 ÷ 2 = 1 262 626 376 + 1;
- 1 262 626 376 ÷ 2 = 631 313 188 + 0;
- 631 313 188 ÷ 2 = 315 656 594 + 0;
- 315 656 594 ÷ 2 = 157 828 297 + 0;
- 157 828 297 ÷ 2 = 78 914 148 + 1;
- 78 914 148 ÷ 2 = 39 457 074 + 0;
- 39 457 074 ÷ 2 = 19 728 537 + 0;
- 19 728 537 ÷ 2 = 9 864 268 + 1;
- 9 864 268 ÷ 2 = 4 932 134 + 0;
- 4 932 134 ÷ 2 = 2 466 067 + 0;
- 2 466 067 ÷ 2 = 1 233 033 + 1;
- 1 233 033 ÷ 2 = 616 516 + 1;
- 616 516 ÷ 2 = 308 258 + 0;
- 308 258 ÷ 2 = 154 129 + 0;
- 154 129 ÷ 2 = 77 064 + 1;
- 77 064 ÷ 2 = 38 532 + 0;
- 38 532 ÷ 2 = 19 266 + 0;
- 19 266 ÷ 2 = 9 633 + 0;
- 9 633 ÷ 2 = 4 816 + 1;
- 4 816 ÷ 2 = 2 408 + 0;
- 2 408 ÷ 2 = 1 204 + 0;
- 1 204 ÷ 2 = 602 + 0;
- 602 ÷ 2 = 301 + 0;
- 301 ÷ 2 = 150 + 1;
- 150 ÷ 2 = 75 + 0;
- 75 ÷ 2 = 37 + 1;
- 37 ÷ 2 = 18 + 1;
- 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.
10 101 011 013(10) = 10 0101 1010 0001 0001 0011 0010 0100 0101(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 34.
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, 34,
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 10 101 011 013(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
10 101 011 013(10) = 0000 0000 0000 0000 0000 0000 0000 0010 0101 1010 0001 0001 0011 0010 0100 0101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.