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;
- 1 644 167 170 ÷ 2 = 822 083 585 + 0;
- 822 083 585 ÷ 2 = 411 041 792 + 1;
- 411 041 792 ÷ 2 = 205 520 896 + 0;
- 205 520 896 ÷ 2 = 102 760 448 + 0;
- 102 760 448 ÷ 2 = 51 380 224 + 0;
- 51 380 224 ÷ 2 = 25 690 112 + 0;
- 25 690 112 ÷ 2 = 12 845 056 + 0;
- 12 845 056 ÷ 2 = 6 422 528 + 0;
- 6 422 528 ÷ 2 = 3 211 264 + 0;
- 3 211 264 ÷ 2 = 1 605 632 + 0;
- 1 605 632 ÷ 2 = 802 816 + 0;
- 802 816 ÷ 2 = 401 408 + 0;
- 401 408 ÷ 2 = 200 704 + 0;
- 200 704 ÷ 2 = 100 352 + 0;
- 100 352 ÷ 2 = 50 176 + 0;
- 50 176 ÷ 2 = 25 088 + 0;
- 25 088 ÷ 2 = 12 544 + 0;
- 12 544 ÷ 2 = 6 272 + 0;
- 6 272 ÷ 2 = 3 136 + 0;
- 3 136 ÷ 2 = 1 568 + 0;
- 1 568 ÷ 2 = 784 + 0;
- 784 ÷ 2 = 392 + 0;
- 392 ÷ 2 = 196 + 0;
- 196 ÷ 2 = 98 + 0;
- 98 ÷ 2 = 49 + 0;
- 49 ÷ 2 = 24 + 1;
- 24 ÷ 2 = 12 + 0;
- 12 ÷ 2 = 6 + 0;
- 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.
1 644 167 170(10) = 110 0010 0000 0000 0000 0000 0000 0010(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 1 644 167 170(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:
1 644 167 170(10) = 0110 0010 0000 0000 0000 0000 0000 0010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.