2. 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;
- 267 578 763 ÷ 2 = 133 789 381 + 1;
- 133 789 381 ÷ 2 = 66 894 690 + 1;
- 66 894 690 ÷ 2 = 33 447 345 + 0;
- 33 447 345 ÷ 2 = 16 723 672 + 1;
- 16 723 672 ÷ 2 = 8 361 836 + 0;
- 8 361 836 ÷ 2 = 4 180 918 + 0;
- 4 180 918 ÷ 2 = 2 090 459 + 0;
- 2 090 459 ÷ 2 = 1 045 229 + 1;
- 1 045 229 ÷ 2 = 522 614 + 1;
- 522 614 ÷ 2 = 261 307 + 0;
- 261 307 ÷ 2 = 130 653 + 1;
- 130 653 ÷ 2 = 65 326 + 1;
- 65 326 ÷ 2 = 32 663 + 0;
- 32 663 ÷ 2 = 16 331 + 1;
- 16 331 ÷ 2 = 8 165 + 1;
- 8 165 ÷ 2 = 4 082 + 1;
- 4 082 ÷ 2 = 2 041 + 0;
- 2 041 ÷ 2 = 1 020 + 1;
- 1 020 ÷ 2 = 510 + 0;
- 510 ÷ 2 = 255 + 0;
- 255 ÷ 2 = 127 + 1;
- 127 ÷ 2 = 63 + 1;
- 63 ÷ 2 = 31 + 1;
- 31 ÷ 2 = 15 + 1;
- 15 ÷ 2 = 7 + 1;
- 7 ÷ 2 = 3 + 1;
- 3 ÷ 2 = 1 + 1;
- 1 ÷ 2 = 0 + 1;
3. Construct the base 2 representation of the positive number:
Take all the remainders starting from the bottom of the list constructed above.
267 578 763(10) = 1111 1111 0010 1110 1101 1000 1011(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 28.
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, 28,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 32.
5. 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:
267 578 763(10) = 0000 1111 1111 0010 1110 1101 1000 1011
6. Get the negative integer number representation:
To get the negative integer number representation on 32 bits (4 Bytes),
... change the first bit (the leftmost), from 0 to 1...
Number -267 578 763(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-267 578 763(10) = 1000 1111 1111 0010 1110 1101 1000 1011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.