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;
- 10 011 111 000 977 ÷ 2 = 5 005 555 500 488 + 1;
- 5 005 555 500 488 ÷ 2 = 2 502 777 750 244 + 0;
- 2 502 777 750 244 ÷ 2 = 1 251 388 875 122 + 0;
- 1 251 388 875 122 ÷ 2 = 625 694 437 561 + 0;
- 625 694 437 561 ÷ 2 = 312 847 218 780 + 1;
- 312 847 218 780 ÷ 2 = 156 423 609 390 + 0;
- 156 423 609 390 ÷ 2 = 78 211 804 695 + 0;
- 78 211 804 695 ÷ 2 = 39 105 902 347 + 1;
- 39 105 902 347 ÷ 2 = 19 552 951 173 + 1;
- 19 552 951 173 ÷ 2 = 9 776 475 586 + 1;
- 9 776 475 586 ÷ 2 = 4 888 237 793 + 0;
- 4 888 237 793 ÷ 2 = 2 444 118 896 + 1;
- 2 444 118 896 ÷ 2 = 1 222 059 448 + 0;
- 1 222 059 448 ÷ 2 = 611 029 724 + 0;
- 611 029 724 ÷ 2 = 305 514 862 + 0;
- 305 514 862 ÷ 2 = 152 757 431 + 0;
- 152 757 431 ÷ 2 = 76 378 715 + 1;
- 76 378 715 ÷ 2 = 38 189 357 + 1;
- 38 189 357 ÷ 2 = 19 094 678 + 1;
- 19 094 678 ÷ 2 = 9 547 339 + 0;
- 9 547 339 ÷ 2 = 4 773 669 + 1;
- 4 773 669 ÷ 2 = 2 386 834 + 1;
- 2 386 834 ÷ 2 = 1 193 417 + 0;
- 1 193 417 ÷ 2 = 596 708 + 1;
- 596 708 ÷ 2 = 298 354 + 0;
- 298 354 ÷ 2 = 149 177 + 0;
- 149 177 ÷ 2 = 74 588 + 1;
- 74 588 ÷ 2 = 37 294 + 0;
- 37 294 ÷ 2 = 18 647 + 0;
- 18 647 ÷ 2 = 9 323 + 1;
- 9 323 ÷ 2 = 4 661 + 1;
- 4 661 ÷ 2 = 2 330 + 1;
- 2 330 ÷ 2 = 1 165 + 0;
- 1 165 ÷ 2 = 582 + 1;
- 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.
10 011 111 000 977(10) = 1001 0001 1010 1110 0100 1011 0111 0000 1011 1001 0001(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 10 011 111 000 977(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
10 011 111 000 977(10) = 0000 0000 0000 0000 0000 1001 0001 1010 1110 0100 1011 0111 0000 1011 1001 0001
Spaces were used to group digits: for binary, by 4, for decimal, by 3.