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;
- 92 233 720 368 514 ÷ 2 = 46 116 860 184 257 + 0;
- 46 116 860 184 257 ÷ 2 = 23 058 430 092 128 + 1;
- 23 058 430 092 128 ÷ 2 = 11 529 215 046 064 + 0;
- 11 529 215 046 064 ÷ 2 = 5 764 607 523 032 + 0;
- 5 764 607 523 032 ÷ 2 = 2 882 303 761 516 + 0;
- 2 882 303 761 516 ÷ 2 = 1 441 151 880 758 + 0;
- 1 441 151 880 758 ÷ 2 = 720 575 940 379 + 0;
- 720 575 940 379 ÷ 2 = 360 287 970 189 + 1;
- 360 287 970 189 ÷ 2 = 180 143 985 094 + 1;
- 180 143 985 094 ÷ 2 = 90 071 992 547 + 0;
- 90 071 992 547 ÷ 2 = 45 035 996 273 + 1;
- 45 035 996 273 ÷ 2 = 22 517 998 136 + 1;
- 22 517 998 136 ÷ 2 = 11 258 999 068 + 0;
- 11 258 999 068 ÷ 2 = 5 629 499 534 + 0;
- 5 629 499 534 ÷ 2 = 2 814 749 767 + 0;
- 2 814 749 767 ÷ 2 = 1 407 374 883 + 1;
- 1 407 374 883 ÷ 2 = 703 687 441 + 1;
- 703 687 441 ÷ 2 = 351 843 720 + 1;
- 351 843 720 ÷ 2 = 175 921 860 + 0;
- 175 921 860 ÷ 2 = 87 960 930 + 0;
- 87 960 930 ÷ 2 = 43 980 465 + 0;
- 43 980 465 ÷ 2 = 21 990 232 + 1;
- 21 990 232 ÷ 2 = 10 995 116 + 0;
- 10 995 116 ÷ 2 = 5 497 558 + 0;
- 5 497 558 ÷ 2 = 2 748 779 + 0;
- 2 748 779 ÷ 2 = 1 374 389 + 1;
- 1 374 389 ÷ 2 = 687 194 + 1;
- 687 194 ÷ 2 = 343 597 + 0;
- 343 597 ÷ 2 = 171 798 + 1;
- 171 798 ÷ 2 = 85 899 + 0;
- 85 899 ÷ 2 = 42 949 + 1;
- 42 949 ÷ 2 = 21 474 + 1;
- 21 474 ÷ 2 = 10 737 + 0;
- 10 737 ÷ 2 = 5 368 + 1;
- 5 368 ÷ 2 = 2 684 + 0;
- 2 684 ÷ 2 = 1 342 + 0;
- 1 342 ÷ 2 = 671 + 0;
- 671 ÷ 2 = 335 + 1;
- 335 ÷ 2 = 167 + 1;
- 167 ÷ 2 = 83 + 1;
- 83 ÷ 2 = 41 + 1;
- 41 ÷ 2 = 20 + 1;
- 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.
92 233 720 368 514(10) = 101 0011 1110 0010 1101 0110 0010 0011 1000 1101 1000 0010(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 92 233 720 368 514(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:
92 233 720 368 514(10) = 0000 0000 0000 0000 0101 0011 1110 0010 1101 0110 0010 0011 1000 1101 1000 0010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.