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;
- 110 111 101 011 110 036 ÷ 2 = 55 055 550 505 555 018 + 0;
- 55 055 550 505 555 018 ÷ 2 = 27 527 775 252 777 509 + 0;
- 27 527 775 252 777 509 ÷ 2 = 13 763 887 626 388 754 + 1;
- 13 763 887 626 388 754 ÷ 2 = 6 881 943 813 194 377 + 0;
- 6 881 943 813 194 377 ÷ 2 = 3 440 971 906 597 188 + 1;
- 3 440 971 906 597 188 ÷ 2 = 1 720 485 953 298 594 + 0;
- 1 720 485 953 298 594 ÷ 2 = 860 242 976 649 297 + 0;
- 860 242 976 649 297 ÷ 2 = 430 121 488 324 648 + 1;
- 430 121 488 324 648 ÷ 2 = 215 060 744 162 324 + 0;
- 215 060 744 162 324 ÷ 2 = 107 530 372 081 162 + 0;
- 107 530 372 081 162 ÷ 2 = 53 765 186 040 581 + 0;
- 53 765 186 040 581 ÷ 2 = 26 882 593 020 290 + 1;
- 26 882 593 020 290 ÷ 2 = 13 441 296 510 145 + 0;
- 13 441 296 510 145 ÷ 2 = 6 720 648 255 072 + 1;
- 6 720 648 255 072 ÷ 2 = 3 360 324 127 536 + 0;
- 3 360 324 127 536 ÷ 2 = 1 680 162 063 768 + 0;
- 1 680 162 063 768 ÷ 2 = 840 081 031 884 + 0;
- 840 081 031 884 ÷ 2 = 420 040 515 942 + 0;
- 420 040 515 942 ÷ 2 = 210 020 257 971 + 0;
- 210 020 257 971 ÷ 2 = 105 010 128 985 + 1;
- 105 010 128 985 ÷ 2 = 52 505 064 492 + 1;
- 52 505 064 492 ÷ 2 = 26 252 532 246 + 0;
- 26 252 532 246 ÷ 2 = 13 126 266 123 + 0;
- 13 126 266 123 ÷ 2 = 6 563 133 061 + 1;
- 6 563 133 061 ÷ 2 = 3 281 566 530 + 1;
- 3 281 566 530 ÷ 2 = 1 640 783 265 + 0;
- 1 640 783 265 ÷ 2 = 820 391 632 + 1;
- 820 391 632 ÷ 2 = 410 195 816 + 0;
- 410 195 816 ÷ 2 = 205 097 908 + 0;
- 205 097 908 ÷ 2 = 102 548 954 + 0;
- 102 548 954 ÷ 2 = 51 274 477 + 0;
- 51 274 477 ÷ 2 = 25 637 238 + 1;
- 25 637 238 ÷ 2 = 12 818 619 + 0;
- 12 818 619 ÷ 2 = 6 409 309 + 1;
- 6 409 309 ÷ 2 = 3 204 654 + 1;
- 3 204 654 ÷ 2 = 1 602 327 + 0;
- 1 602 327 ÷ 2 = 801 163 + 1;
- 801 163 ÷ 2 = 400 581 + 1;
- 400 581 ÷ 2 = 200 290 + 1;
- 200 290 ÷ 2 = 100 145 + 0;
- 100 145 ÷ 2 = 50 072 + 1;
- 50 072 ÷ 2 = 25 036 + 0;
- 25 036 ÷ 2 = 12 518 + 0;
- 12 518 ÷ 2 = 6 259 + 0;
- 6 259 ÷ 2 = 3 129 + 1;
- 3 129 ÷ 2 = 1 564 + 1;
- 1 564 ÷ 2 = 782 + 0;
- 782 ÷ 2 = 391 + 0;
- 391 ÷ 2 = 195 + 1;
- 195 ÷ 2 = 97 + 1;
- 97 ÷ 2 = 48 + 1;
- 48 ÷ 2 = 24 + 0;
- 24 ÷ 2 = 12 + 0;
- 12 ÷ 2 = 6 + 0;
- 6 ÷ 2 = 3 + 0;
- 3 ÷ 2 = 1 + 1;
- 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.
110 111 101 011 110 036(10) = 1 1000 0111 0011 0001 0111 0110 1000 0101 1001 1000 0010 1000 1001 0100(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 57.
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, 57,
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 110 111 101 011 110 036(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:
110 111 101 011 110 036(10) = 0000 0001 1000 0111 0011 0001 0111 0110 1000 0101 1001 1000 0010 1000 1001 0100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.