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;
- 1 010 101 101 010 000 ÷ 2 = 505 050 550 505 000 + 0;
- 505 050 550 505 000 ÷ 2 = 252 525 275 252 500 + 0;
- 252 525 275 252 500 ÷ 2 = 126 262 637 626 250 + 0;
- 126 262 637 626 250 ÷ 2 = 63 131 318 813 125 + 0;
- 63 131 318 813 125 ÷ 2 = 31 565 659 406 562 + 1;
- 31 565 659 406 562 ÷ 2 = 15 782 829 703 281 + 0;
- 15 782 829 703 281 ÷ 2 = 7 891 414 851 640 + 1;
- 7 891 414 851 640 ÷ 2 = 3 945 707 425 820 + 0;
- 3 945 707 425 820 ÷ 2 = 1 972 853 712 910 + 0;
- 1 972 853 712 910 ÷ 2 = 986 426 856 455 + 0;
- 986 426 856 455 ÷ 2 = 493 213 428 227 + 1;
- 493 213 428 227 ÷ 2 = 246 606 714 113 + 1;
- 246 606 714 113 ÷ 2 = 123 303 357 056 + 1;
- 123 303 357 056 ÷ 2 = 61 651 678 528 + 0;
- 61 651 678 528 ÷ 2 = 30 825 839 264 + 0;
- 30 825 839 264 ÷ 2 = 15 412 919 632 + 0;
- 15 412 919 632 ÷ 2 = 7 706 459 816 + 0;
- 7 706 459 816 ÷ 2 = 3 853 229 908 + 0;
- 3 853 229 908 ÷ 2 = 1 926 614 954 + 0;
- 1 926 614 954 ÷ 2 = 963 307 477 + 0;
- 963 307 477 ÷ 2 = 481 653 738 + 1;
- 481 653 738 ÷ 2 = 240 826 869 + 0;
- 240 826 869 ÷ 2 = 120 413 434 + 1;
- 120 413 434 ÷ 2 = 60 206 717 + 0;
- 60 206 717 ÷ 2 = 30 103 358 + 1;
- 30 103 358 ÷ 2 = 15 051 679 + 0;
- 15 051 679 ÷ 2 = 7 525 839 + 1;
- 7 525 839 ÷ 2 = 3 762 919 + 1;
- 3 762 919 ÷ 2 = 1 881 459 + 1;
- 1 881 459 ÷ 2 = 940 729 + 1;
- 940 729 ÷ 2 = 470 364 + 1;
- 470 364 ÷ 2 = 235 182 + 0;
- 235 182 ÷ 2 = 117 591 + 0;
- 117 591 ÷ 2 = 58 795 + 1;
- 58 795 ÷ 2 = 29 397 + 1;
- 29 397 ÷ 2 = 14 698 + 1;
- 14 698 ÷ 2 = 7 349 + 0;
- 7 349 ÷ 2 = 3 674 + 1;
- 3 674 ÷ 2 = 1 837 + 0;
- 1 837 ÷ 2 = 918 + 1;
- 918 ÷ 2 = 459 + 0;
- 459 ÷ 2 = 229 + 1;
- 229 ÷ 2 = 114 + 1;
- 114 ÷ 2 = 57 + 0;
- 57 ÷ 2 = 28 + 1;
- 28 ÷ 2 = 14 + 0;
- 14 ÷ 2 = 7 + 0;
- 7 ÷ 2 = 3 + 1;
- 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.
1 010 101 101 010 000(10) = 11 1001 0110 1010 1110 0111 1101 0101 0000 0001 1100 0101 0000(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 50.
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, 50,
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 1 010 101 101 010 000(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:
1 010 101 101 010 000(10) = 0000 0000 0000 0011 1001 0110 1010 1110 0111 1101 0101 0000 0001 1100 0101 0000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.