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;
- 110 100 001 010 101 058 ÷ 2 = 55 050 000 505 050 529 + 0;
- 55 050 000 505 050 529 ÷ 2 = 27 525 000 252 525 264 + 1;
- 27 525 000 252 525 264 ÷ 2 = 13 762 500 126 262 632 + 0;
- 13 762 500 126 262 632 ÷ 2 = 6 881 250 063 131 316 + 0;
- 6 881 250 063 131 316 ÷ 2 = 3 440 625 031 565 658 + 0;
- 3 440 625 031 565 658 ÷ 2 = 1 720 312 515 782 829 + 0;
- 1 720 312 515 782 829 ÷ 2 = 860 156 257 891 414 + 1;
- 860 156 257 891 414 ÷ 2 = 430 078 128 945 707 + 0;
- 430 078 128 945 707 ÷ 2 = 215 039 064 472 853 + 1;
- 215 039 064 472 853 ÷ 2 = 107 519 532 236 426 + 1;
- 107 519 532 236 426 ÷ 2 = 53 759 766 118 213 + 0;
- 53 759 766 118 213 ÷ 2 = 26 879 883 059 106 + 1;
- 26 879 883 059 106 ÷ 2 = 13 439 941 529 553 + 0;
- 13 439 941 529 553 ÷ 2 = 6 719 970 764 776 + 1;
- 6 719 970 764 776 ÷ 2 = 3 359 985 382 388 + 0;
- 3 359 985 382 388 ÷ 2 = 1 679 992 691 194 + 0;
- 1 679 992 691 194 ÷ 2 = 839 996 345 597 + 0;
- 839 996 345 597 ÷ 2 = 419 998 172 798 + 1;
- 419 998 172 798 ÷ 2 = 209 999 086 399 + 0;
- 209 999 086 399 ÷ 2 = 104 999 543 199 + 1;
- 104 999 543 199 ÷ 2 = 52 499 771 599 + 1;
- 52 499 771 599 ÷ 2 = 26 249 885 799 + 1;
- 26 249 885 799 ÷ 2 = 13 124 942 899 + 1;
- 13 124 942 899 ÷ 2 = 6 562 471 449 + 1;
- 6 562 471 449 ÷ 2 = 3 281 235 724 + 1;
- 3 281 235 724 ÷ 2 = 1 640 617 862 + 0;
- 1 640 617 862 ÷ 2 = 820 308 931 + 0;
- 820 308 931 ÷ 2 = 410 154 465 + 1;
- 410 154 465 ÷ 2 = 205 077 232 + 1;
- 205 077 232 ÷ 2 = 102 538 616 + 0;
- 102 538 616 ÷ 2 = 51 269 308 + 0;
- 51 269 308 ÷ 2 = 25 634 654 + 0;
- 25 634 654 ÷ 2 = 12 817 327 + 0;
- 12 817 327 ÷ 2 = 6 408 663 + 1;
- 6 408 663 ÷ 2 = 3 204 331 + 1;
- 3 204 331 ÷ 2 = 1 602 165 + 1;
- 1 602 165 ÷ 2 = 801 082 + 1;
- 801 082 ÷ 2 = 400 541 + 0;
- 400 541 ÷ 2 = 200 270 + 1;
- 200 270 ÷ 2 = 100 135 + 0;
- 100 135 ÷ 2 = 50 067 + 1;
- 50 067 ÷ 2 = 25 033 + 1;
- 25 033 ÷ 2 = 12 516 + 1;
- 12 516 ÷ 2 = 6 258 + 0;
- 6 258 ÷ 2 = 3 129 + 0;
- 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.
110 100 001 010 101 058(10) = 1 1000 0111 0010 0111 0101 1110 0001 1001 1111 1010 0010 1011 0100 0010(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 110 100 001 010 101 058(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:
110 100 001 010 101 058(10) = 0000 0001 1000 0111 0010 0111 0101 1110 0001 1001 1111 1010 0010 1011 0100 0010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.