2. 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;
- 10 654 324 631 552 ÷ 2 = 5 327 162 315 776 + 0;
- 5 327 162 315 776 ÷ 2 = 2 663 581 157 888 + 0;
- 2 663 581 157 888 ÷ 2 = 1 331 790 578 944 + 0;
- 1 331 790 578 944 ÷ 2 = 665 895 289 472 + 0;
- 665 895 289 472 ÷ 2 = 332 947 644 736 + 0;
- 332 947 644 736 ÷ 2 = 166 473 822 368 + 0;
- 166 473 822 368 ÷ 2 = 83 236 911 184 + 0;
- 83 236 911 184 ÷ 2 = 41 618 455 592 + 0;
- 41 618 455 592 ÷ 2 = 20 809 227 796 + 0;
- 20 809 227 796 ÷ 2 = 10 404 613 898 + 0;
- 10 404 613 898 ÷ 2 = 5 202 306 949 + 0;
- 5 202 306 949 ÷ 2 = 2 601 153 474 + 1;
- 2 601 153 474 ÷ 2 = 1 300 576 737 + 0;
- 1 300 576 737 ÷ 2 = 650 288 368 + 1;
- 650 288 368 ÷ 2 = 325 144 184 + 0;
- 325 144 184 ÷ 2 = 162 572 092 + 0;
- 162 572 092 ÷ 2 = 81 286 046 + 0;
- 81 286 046 ÷ 2 = 40 643 023 + 0;
- 40 643 023 ÷ 2 = 20 321 511 + 1;
- 20 321 511 ÷ 2 = 10 160 755 + 1;
- 10 160 755 ÷ 2 = 5 080 377 + 1;
- 5 080 377 ÷ 2 = 2 540 188 + 1;
- 2 540 188 ÷ 2 = 1 270 094 + 0;
- 1 270 094 ÷ 2 = 635 047 + 0;
- 635 047 ÷ 2 = 317 523 + 1;
- 317 523 ÷ 2 = 158 761 + 1;
- 158 761 ÷ 2 = 79 380 + 1;
- 79 380 ÷ 2 = 39 690 + 0;
- 39 690 ÷ 2 = 19 845 + 0;
- 19 845 ÷ 2 = 9 922 + 1;
- 9 922 ÷ 2 = 4 961 + 0;
- 4 961 ÷ 2 = 2 480 + 1;
- 2 480 ÷ 2 = 1 240 + 0;
- 1 240 ÷ 2 = 620 + 0;
- 620 ÷ 2 = 310 + 0;
- 310 ÷ 2 = 155 + 0;
- 155 ÷ 2 = 77 + 1;
- 77 ÷ 2 = 38 + 1;
- 38 ÷ 2 = 19 + 0;
- 19 ÷ 2 = 9 + 1;
- 9 ÷ 2 = 4 + 1;
- 4 ÷ 2 = 2 + 0;
- 2 ÷ 2 = 1 + 0;
- 1 ÷ 2 = 0 + 1;
3. Construct the base 2 representation of the positive number:
Take all the remainders starting from the bottom of the list constructed above.
10 654 324 631 552(10) = 1001 1011 0000 1010 0111 0011 1100 0010 1000 0000 0000(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 44.
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, 44,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 64.
5. 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:
10 654 324 631 552(10) = 0000 0000 0000 0000 0000 1001 1011 0000 1010 0111 0011 1100 0010 1000 0000 0000
6. Get the negative integer number representation:
To get the negative integer number representation on 64 bits (8 Bytes),
... change the first bit (the leftmost), from 0 to 1...
Number -10 654 324 631 552(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-10 654 324 631 552(10) = 1000 0000 0000 0000 0000 1001 1011 0000 1010 0111 0011 1100 0010 1000 0000 0000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.