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;
- 1 010 111 111 100 150 ÷ 2 = 505 055 555 550 075 + 0;
- 505 055 555 550 075 ÷ 2 = 252 527 777 775 037 + 1;
- 252 527 777 775 037 ÷ 2 = 126 263 888 887 518 + 1;
- 126 263 888 887 518 ÷ 2 = 63 131 944 443 759 + 0;
- 63 131 944 443 759 ÷ 2 = 31 565 972 221 879 + 1;
- 31 565 972 221 879 ÷ 2 = 15 782 986 110 939 + 1;
- 15 782 986 110 939 ÷ 2 = 7 891 493 055 469 + 1;
- 7 891 493 055 469 ÷ 2 = 3 945 746 527 734 + 1;
- 3 945 746 527 734 ÷ 2 = 1 972 873 263 867 + 0;
- 1 972 873 263 867 ÷ 2 = 986 436 631 933 + 1;
- 986 436 631 933 ÷ 2 = 493 218 315 966 + 1;
- 493 218 315 966 ÷ 2 = 246 609 157 983 + 0;
- 246 609 157 983 ÷ 2 = 123 304 578 991 + 1;
- 123 304 578 991 ÷ 2 = 61 652 289 495 + 1;
- 61 652 289 495 ÷ 2 = 30 826 144 747 + 1;
- 30 826 144 747 ÷ 2 = 15 413 072 373 + 1;
- 15 413 072 373 ÷ 2 = 7 706 536 186 + 1;
- 7 706 536 186 ÷ 2 = 3 853 268 093 + 0;
- 3 853 268 093 ÷ 2 = 1 926 634 046 + 1;
- 1 926 634 046 ÷ 2 = 963 317 023 + 0;
- 963 317 023 ÷ 2 = 481 658 511 + 1;
- 481 658 511 ÷ 2 = 240 829 255 + 1;
- 240 829 255 ÷ 2 = 120 414 627 + 1;
- 120 414 627 ÷ 2 = 60 207 313 + 1;
- 60 207 313 ÷ 2 = 30 103 656 + 1;
- 30 103 656 ÷ 2 = 15 051 828 + 0;
- 15 051 828 ÷ 2 = 7 525 914 + 0;
- 7 525 914 ÷ 2 = 3 762 957 + 0;
- 3 762 957 ÷ 2 = 1 881 478 + 1;
- 1 881 478 ÷ 2 = 940 739 + 0;
- 940 739 ÷ 2 = 470 369 + 1;
- 470 369 ÷ 2 = 235 184 + 1;
- 235 184 ÷ 2 = 117 592 + 0;
- 117 592 ÷ 2 = 58 796 + 0;
- 58 796 ÷ 2 = 29 398 + 0;
- 29 398 ÷ 2 = 14 699 + 0;
- 14 699 ÷ 2 = 7 349 + 1;
- 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.
1 010 111 111 100 150(10) = 11 1001 0110 1011 0000 1101 0001 1111 0101 1111 0110 1111 0110(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 1 010 111 111 100 150(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:
1 010 111 111 100 150(10) = 0000 0000 0000 0011 1001 0110 1011 0000 1101 0001 1111 0101 1111 0110 1111 0110
Spaces were used to group digits: for binary, by 4, for decimal, by 3.