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;
- 9 876 540 116 ÷ 2 = 4 938 270 058 + 0;
- 4 938 270 058 ÷ 2 = 2 469 135 029 + 0;
- 2 469 135 029 ÷ 2 = 1 234 567 514 + 1;
- 1 234 567 514 ÷ 2 = 617 283 757 + 0;
- 617 283 757 ÷ 2 = 308 641 878 + 1;
- 308 641 878 ÷ 2 = 154 320 939 + 0;
- 154 320 939 ÷ 2 = 77 160 469 + 1;
- 77 160 469 ÷ 2 = 38 580 234 + 1;
- 38 580 234 ÷ 2 = 19 290 117 + 0;
- 19 290 117 ÷ 2 = 9 645 058 + 1;
- 9 645 058 ÷ 2 = 4 822 529 + 0;
- 4 822 529 ÷ 2 = 2 411 264 + 1;
- 2 411 264 ÷ 2 = 1 205 632 + 0;
- 1 205 632 ÷ 2 = 602 816 + 0;
- 602 816 ÷ 2 = 301 408 + 0;
- 301 408 ÷ 2 = 150 704 + 0;
- 150 704 ÷ 2 = 75 352 + 0;
- 75 352 ÷ 2 = 37 676 + 0;
- 37 676 ÷ 2 = 18 838 + 0;
- 18 838 ÷ 2 = 9 419 + 0;
- 9 419 ÷ 2 = 4 709 + 1;
- 4 709 ÷ 2 = 2 354 + 1;
- 2 354 ÷ 2 = 1 177 + 0;
- 1 177 ÷ 2 = 588 + 1;
- 588 ÷ 2 = 294 + 0;
- 294 ÷ 2 = 147 + 0;
- 147 ÷ 2 = 73 + 1;
- 73 ÷ 2 = 36 + 1;
- 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.
9 876 540 116(10) = 10 0100 1100 1011 0000 0000 1010 1101 0100(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 9 876 540 116(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
9 876 540 116(10) = 0000 0000 0000 0000 0000 0000 0000 0010 0100 1100 1011 0000 0000 1010 1101 0100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.