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;
- 696 569 654 286 ÷ 2 = 348 284 827 143 + 0;
- 348 284 827 143 ÷ 2 = 174 142 413 571 + 1;
- 174 142 413 571 ÷ 2 = 87 071 206 785 + 1;
- 87 071 206 785 ÷ 2 = 43 535 603 392 + 1;
- 43 535 603 392 ÷ 2 = 21 767 801 696 + 0;
- 21 767 801 696 ÷ 2 = 10 883 900 848 + 0;
- 10 883 900 848 ÷ 2 = 5 441 950 424 + 0;
- 5 441 950 424 ÷ 2 = 2 720 975 212 + 0;
- 2 720 975 212 ÷ 2 = 1 360 487 606 + 0;
- 1 360 487 606 ÷ 2 = 680 243 803 + 0;
- 680 243 803 ÷ 2 = 340 121 901 + 1;
- 340 121 901 ÷ 2 = 170 060 950 + 1;
- 170 060 950 ÷ 2 = 85 030 475 + 0;
- 85 030 475 ÷ 2 = 42 515 237 + 1;
- 42 515 237 ÷ 2 = 21 257 618 + 1;
- 21 257 618 ÷ 2 = 10 628 809 + 0;
- 10 628 809 ÷ 2 = 5 314 404 + 1;
- 5 314 404 ÷ 2 = 2 657 202 + 0;
- 2 657 202 ÷ 2 = 1 328 601 + 0;
- 1 328 601 ÷ 2 = 664 300 + 1;
- 664 300 ÷ 2 = 332 150 + 0;
- 332 150 ÷ 2 = 166 075 + 0;
- 166 075 ÷ 2 = 83 037 + 1;
- 83 037 ÷ 2 = 41 518 + 1;
- 41 518 ÷ 2 = 20 759 + 0;
- 20 759 ÷ 2 = 10 379 + 1;
- 10 379 ÷ 2 = 5 189 + 1;
- 5 189 ÷ 2 = 2 594 + 1;
- 2 594 ÷ 2 = 1 297 + 0;
- 1 297 ÷ 2 = 648 + 1;
- 648 ÷ 2 = 324 + 0;
- 324 ÷ 2 = 162 + 0;
- 162 ÷ 2 = 81 + 0;
- 81 ÷ 2 = 40 + 1;
- 40 ÷ 2 = 20 + 0;
- 20 ÷ 2 = 10 + 0;
- 10 ÷ 2 = 5 + 0;
- 5 ÷ 2 = 2 + 1;
- 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.
696 569 654 286(10) = 1010 0010 0010 1110 1100 1001 0110 1100 0000 1110(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 40.
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, 40,
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 696 569 654 286(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:
696 569 654 286(10) = 0000 0000 0000 0000 0000 0000 1010 0010 0010 1110 1100 1001 0110 1100 0000 1110
Spaces were used to group digits: for binary, by 4, for decimal, by 3.