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;
- 1 094 861 595 ÷ 2 = 547 430 797 + 1;
- 547 430 797 ÷ 2 = 273 715 398 + 1;
- 273 715 398 ÷ 2 = 136 857 699 + 0;
- 136 857 699 ÷ 2 = 68 428 849 + 1;
- 68 428 849 ÷ 2 = 34 214 424 + 1;
- 34 214 424 ÷ 2 = 17 107 212 + 0;
- 17 107 212 ÷ 2 = 8 553 606 + 0;
- 8 553 606 ÷ 2 = 4 276 803 + 0;
- 4 276 803 ÷ 2 = 2 138 401 + 1;
- 2 138 401 ÷ 2 = 1 069 200 + 1;
- 1 069 200 ÷ 2 = 534 600 + 0;
- 534 600 ÷ 2 = 267 300 + 0;
- 267 300 ÷ 2 = 133 650 + 0;
- 133 650 ÷ 2 = 66 825 + 0;
- 66 825 ÷ 2 = 33 412 + 1;
- 33 412 ÷ 2 = 16 706 + 0;
- 16 706 ÷ 2 = 8 353 + 0;
- 8 353 ÷ 2 = 4 176 + 1;
- 4 176 ÷ 2 = 2 088 + 0;
- 2 088 ÷ 2 = 1 044 + 0;
- 1 044 ÷ 2 = 522 + 0;
- 522 ÷ 2 = 261 + 0;
- 261 ÷ 2 = 130 + 1;
- 130 ÷ 2 = 65 + 0;
- 65 ÷ 2 = 32 + 1;
- 32 ÷ 2 = 16 + 0;
- 16 ÷ 2 = 8 + 0;
- 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.
1 094 861 595(10) = 100 0001 0100 0010 0100 0011 0001 1011(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) 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, 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 1 094 861 595(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:
1 094 861 595(10) = 0100 0001 0100 0010 0100 0011 0001 1011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.