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;
- 1 861 152 565 ÷ 2 = 930 576 282 + 1;
- 930 576 282 ÷ 2 = 465 288 141 + 0;
- 465 288 141 ÷ 2 = 232 644 070 + 1;
- 232 644 070 ÷ 2 = 116 322 035 + 0;
- 116 322 035 ÷ 2 = 58 161 017 + 1;
- 58 161 017 ÷ 2 = 29 080 508 + 1;
- 29 080 508 ÷ 2 = 14 540 254 + 0;
- 14 540 254 ÷ 2 = 7 270 127 + 0;
- 7 270 127 ÷ 2 = 3 635 063 + 1;
- 3 635 063 ÷ 2 = 1 817 531 + 1;
- 1 817 531 ÷ 2 = 908 765 + 1;
- 908 765 ÷ 2 = 454 382 + 1;
- 454 382 ÷ 2 = 227 191 + 0;
- 227 191 ÷ 2 = 113 595 + 1;
- 113 595 ÷ 2 = 56 797 + 1;
- 56 797 ÷ 2 = 28 398 + 1;
- 28 398 ÷ 2 = 14 199 + 0;
- 14 199 ÷ 2 = 7 099 + 1;
- 7 099 ÷ 2 = 3 549 + 1;
- 3 549 ÷ 2 = 1 774 + 1;
- 1 774 ÷ 2 = 887 + 0;
- 887 ÷ 2 = 443 + 1;
- 443 ÷ 2 = 221 + 1;
- 221 ÷ 2 = 110 + 1;
- 110 ÷ 2 = 55 + 0;
- 55 ÷ 2 = 27 + 1;
- 27 ÷ 2 = 13 + 1;
- 13 ÷ 2 = 6 + 1;
- 6 ÷ 2 = 3 + 0;
- 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.
1 861 152 565(10) = 110 1110 1110 1110 1110 1111 0011 0101(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 31.
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, 31,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 32.
4. Get the positive binary computer representation on 32 bits (4 Bytes):
If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 32:
Number 1 861 152 565(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
1 861 152 565(10) = 0110 1110 1110 1110 1110 1111 0011 0101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.