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;
- 10 001 110 110 068 ÷ 2 = 5 000 555 055 034 + 0;
- 5 000 555 055 034 ÷ 2 = 2 500 277 527 517 + 0;
- 2 500 277 527 517 ÷ 2 = 1 250 138 763 758 + 1;
- 1 250 138 763 758 ÷ 2 = 625 069 381 879 + 0;
- 625 069 381 879 ÷ 2 = 312 534 690 939 + 1;
- 312 534 690 939 ÷ 2 = 156 267 345 469 + 1;
- 156 267 345 469 ÷ 2 = 78 133 672 734 + 1;
- 78 133 672 734 ÷ 2 = 39 066 836 367 + 0;
- 39 066 836 367 ÷ 2 = 19 533 418 183 + 1;
- 19 533 418 183 ÷ 2 = 9 766 709 091 + 1;
- 9 766 709 091 ÷ 2 = 4 883 354 545 + 1;
- 4 883 354 545 ÷ 2 = 2 441 677 272 + 1;
- 2 441 677 272 ÷ 2 = 1 220 838 636 + 0;
- 1 220 838 636 ÷ 2 = 610 419 318 + 0;
- 610 419 318 ÷ 2 = 305 209 659 + 0;
- 305 209 659 ÷ 2 = 152 604 829 + 1;
- 152 604 829 ÷ 2 = 76 302 414 + 1;
- 76 302 414 ÷ 2 = 38 151 207 + 0;
- 38 151 207 ÷ 2 = 19 075 603 + 1;
- 19 075 603 ÷ 2 = 9 537 801 + 1;
- 9 537 801 ÷ 2 = 4 768 900 + 1;
- 4 768 900 ÷ 2 = 2 384 450 + 0;
- 2 384 450 ÷ 2 = 1 192 225 + 0;
- 1 192 225 ÷ 2 = 596 112 + 1;
- 596 112 ÷ 2 = 298 056 + 0;
- 298 056 ÷ 2 = 149 028 + 0;
- 149 028 ÷ 2 = 74 514 + 0;
- 74 514 ÷ 2 = 37 257 + 0;
- 37 257 ÷ 2 = 18 628 + 1;
- 18 628 ÷ 2 = 9 314 + 0;
- 9 314 ÷ 2 = 4 657 + 0;
- 4 657 ÷ 2 = 2 328 + 1;
- 2 328 ÷ 2 = 1 164 + 0;
- 1 164 ÷ 2 = 582 + 0;
- 582 ÷ 2 = 291 + 0;
- 291 ÷ 2 = 145 + 1;
- 145 ÷ 2 = 72 + 1;
- 72 ÷ 2 = 36 + 0;
- 36 ÷ 2 = 18 + 0;
- 18 ÷ 2 = 9 + 0;
- 9 ÷ 2 = 4 + 1;
- 4 ÷ 2 = 2 + 0;
- 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.
10 001 110 110 068(10) = 1001 0001 1000 1001 0000 1001 1101 1000 1111 0111 0100(2)
3. 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.
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 10 001 110 110 068(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
10 001 110 110 068(10) = 0000 0000 0000 0000 0000 1001 0001 1000 1001 0000 1001 1101 1000 1111 0111 0100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.