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;
- 2 346 683 274 ÷ 2 = 1 173 341 637 + 0;
- 1 173 341 637 ÷ 2 = 586 670 818 + 1;
- 586 670 818 ÷ 2 = 293 335 409 + 0;
- 293 335 409 ÷ 2 = 146 667 704 + 1;
- 146 667 704 ÷ 2 = 73 333 852 + 0;
- 73 333 852 ÷ 2 = 36 666 926 + 0;
- 36 666 926 ÷ 2 = 18 333 463 + 0;
- 18 333 463 ÷ 2 = 9 166 731 + 1;
- 9 166 731 ÷ 2 = 4 583 365 + 1;
- 4 583 365 ÷ 2 = 2 291 682 + 1;
- 2 291 682 ÷ 2 = 1 145 841 + 0;
- 1 145 841 ÷ 2 = 572 920 + 1;
- 572 920 ÷ 2 = 286 460 + 0;
- 286 460 ÷ 2 = 143 230 + 0;
- 143 230 ÷ 2 = 71 615 + 0;
- 71 615 ÷ 2 = 35 807 + 1;
- 35 807 ÷ 2 = 17 903 + 1;
- 17 903 ÷ 2 = 8 951 + 1;
- 8 951 ÷ 2 = 4 475 + 1;
- 4 475 ÷ 2 = 2 237 + 1;
- 2 237 ÷ 2 = 1 118 + 1;
- 1 118 ÷ 2 = 559 + 0;
- 559 ÷ 2 = 279 + 1;
- 279 ÷ 2 = 139 + 1;
- 139 ÷ 2 = 69 + 1;
- 69 ÷ 2 = 34 + 1;
- 34 ÷ 2 = 17 + 0;
- 17 ÷ 2 = 8 + 1;
- 8 ÷ 2 = 4 + 0;
- 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.
2 346 683 274(10) = 1000 1011 1101 1111 1000 1011 1000 1010(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 32.
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, 32,
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 2 346 683 274(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:
2 346 683 274(10) = 0000 0000 0000 0000 0000 0000 0000 0000 1000 1011 1101 1111 1000 1011 1000 1010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.