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;
- 100 010 110 075 ÷ 2 = 50 005 055 037 + 1;
- 50 005 055 037 ÷ 2 = 25 002 527 518 + 1;
- 25 002 527 518 ÷ 2 = 12 501 263 759 + 0;
- 12 501 263 759 ÷ 2 = 6 250 631 879 + 1;
- 6 250 631 879 ÷ 2 = 3 125 315 939 + 1;
- 3 125 315 939 ÷ 2 = 1 562 657 969 + 1;
- 1 562 657 969 ÷ 2 = 781 328 984 + 1;
- 781 328 984 ÷ 2 = 390 664 492 + 0;
- 390 664 492 ÷ 2 = 195 332 246 + 0;
- 195 332 246 ÷ 2 = 97 666 123 + 0;
- 97 666 123 ÷ 2 = 48 833 061 + 1;
- 48 833 061 ÷ 2 = 24 416 530 + 1;
- 24 416 530 ÷ 2 = 12 208 265 + 0;
- 12 208 265 ÷ 2 = 6 104 132 + 1;
- 6 104 132 ÷ 2 = 3 052 066 + 0;
- 3 052 066 ÷ 2 = 1 526 033 + 0;
- 1 526 033 ÷ 2 = 763 016 + 1;
- 763 016 ÷ 2 = 381 508 + 0;
- 381 508 ÷ 2 = 190 754 + 0;
- 190 754 ÷ 2 = 95 377 + 0;
- 95 377 ÷ 2 = 47 688 + 1;
- 47 688 ÷ 2 = 23 844 + 0;
- 23 844 ÷ 2 = 11 922 + 0;
- 11 922 ÷ 2 = 5 961 + 0;
- 5 961 ÷ 2 = 2 980 + 1;
- 2 980 ÷ 2 = 1 490 + 0;
- 1 490 ÷ 2 = 745 + 0;
- 745 ÷ 2 = 372 + 1;
- 372 ÷ 2 = 186 + 0;
- 186 ÷ 2 = 93 + 0;
- 93 ÷ 2 = 46 + 1;
- 46 ÷ 2 = 23 + 0;
- 23 ÷ 2 = 11 + 1;
- 11 ÷ 2 = 5 + 1;
- 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.
100 010 110 075(10) = 1 0111 0100 1001 0001 0001 0010 1100 0111 1011(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 37.
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, 37,
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 100 010 110 075(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:
100 010 110 075(10) = 0000 0000 0000 0000 0000 0000 0001 0111 0100 1001 0001 0001 0010 1100 0111 1011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.