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;
- 101 100 101 110 006 ÷ 2 = 50 550 050 555 003 + 0;
- 50 550 050 555 003 ÷ 2 = 25 275 025 277 501 + 1;
- 25 275 025 277 501 ÷ 2 = 12 637 512 638 750 + 1;
- 12 637 512 638 750 ÷ 2 = 6 318 756 319 375 + 0;
- 6 318 756 319 375 ÷ 2 = 3 159 378 159 687 + 1;
- 3 159 378 159 687 ÷ 2 = 1 579 689 079 843 + 1;
- 1 579 689 079 843 ÷ 2 = 789 844 539 921 + 1;
- 789 844 539 921 ÷ 2 = 394 922 269 960 + 1;
- 394 922 269 960 ÷ 2 = 197 461 134 980 + 0;
- 197 461 134 980 ÷ 2 = 98 730 567 490 + 0;
- 98 730 567 490 ÷ 2 = 49 365 283 745 + 0;
- 49 365 283 745 ÷ 2 = 24 682 641 872 + 1;
- 24 682 641 872 ÷ 2 = 12 341 320 936 + 0;
- 12 341 320 936 ÷ 2 = 6 170 660 468 + 0;
- 6 170 660 468 ÷ 2 = 3 085 330 234 + 0;
- 3 085 330 234 ÷ 2 = 1 542 665 117 + 0;
- 1 542 665 117 ÷ 2 = 771 332 558 + 1;
- 771 332 558 ÷ 2 = 385 666 279 + 0;
- 385 666 279 ÷ 2 = 192 833 139 + 1;
- 192 833 139 ÷ 2 = 96 416 569 + 1;
- 96 416 569 ÷ 2 = 48 208 284 + 1;
- 48 208 284 ÷ 2 = 24 104 142 + 0;
- 24 104 142 ÷ 2 = 12 052 071 + 0;
- 12 052 071 ÷ 2 = 6 026 035 + 1;
- 6 026 035 ÷ 2 = 3 013 017 + 1;
- 3 013 017 ÷ 2 = 1 506 508 + 1;
- 1 506 508 ÷ 2 = 753 254 + 0;
- 753 254 ÷ 2 = 376 627 + 0;
- 376 627 ÷ 2 = 188 313 + 1;
- 188 313 ÷ 2 = 94 156 + 1;
- 94 156 ÷ 2 = 47 078 + 0;
- 47 078 ÷ 2 = 23 539 + 0;
- 23 539 ÷ 2 = 11 769 + 1;
- 11 769 ÷ 2 = 5 884 + 1;
- 5 884 ÷ 2 = 2 942 + 0;
- 2 942 ÷ 2 = 1 471 + 0;
- 1 471 ÷ 2 = 735 + 1;
- 735 ÷ 2 = 367 + 1;
- 367 ÷ 2 = 183 + 1;
- 183 ÷ 2 = 91 + 1;
- 91 ÷ 2 = 45 + 1;
- 45 ÷ 2 = 22 + 1;
- 22 ÷ 2 = 11 + 0;
- 11 ÷ 2 = 5 + 1;
- 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.
101 100 101 110 006(10) = 101 1011 1111 0011 0011 0011 1001 1101 0000 1000 1111 0110(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 47.
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, 47,
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 101 100 101 110 006(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:
101 100 101 110 006(10) = 0000 0000 0000 0000 0101 1011 1111 0011 0011 0011 1001 1101 0000 1000 1111 0110
Spaces were used to group digits: for binary, by 4, for decimal, by 3.