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;
- 2 576 341 550 ÷ 2 = 1 288 170 775 + 0;
- 1 288 170 775 ÷ 2 = 644 085 387 + 1;
- 644 085 387 ÷ 2 = 322 042 693 + 1;
- 322 042 693 ÷ 2 = 161 021 346 + 1;
- 161 021 346 ÷ 2 = 80 510 673 + 0;
- 80 510 673 ÷ 2 = 40 255 336 + 1;
- 40 255 336 ÷ 2 = 20 127 668 + 0;
- 20 127 668 ÷ 2 = 10 063 834 + 0;
- 10 063 834 ÷ 2 = 5 031 917 + 0;
- 5 031 917 ÷ 2 = 2 515 958 + 1;
- 2 515 958 ÷ 2 = 1 257 979 + 0;
- 1 257 979 ÷ 2 = 628 989 + 1;
- 628 989 ÷ 2 = 314 494 + 1;
- 314 494 ÷ 2 = 157 247 + 0;
- 157 247 ÷ 2 = 78 623 + 1;
- 78 623 ÷ 2 = 39 311 + 1;
- 39 311 ÷ 2 = 19 655 + 1;
- 19 655 ÷ 2 = 9 827 + 1;
- 9 827 ÷ 2 = 4 913 + 1;
- 4 913 ÷ 2 = 2 456 + 1;
- 2 456 ÷ 2 = 1 228 + 0;
- 1 228 ÷ 2 = 614 + 0;
- 614 ÷ 2 = 307 + 0;
- 307 ÷ 2 = 153 + 1;
- 153 ÷ 2 = 76 + 1;
- 76 ÷ 2 = 38 + 0;
- 38 ÷ 2 = 19 + 0;
- 19 ÷ 2 = 9 + 1;
- 9 ÷ 2 = 4 + 1;
- 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.
2 576 341 550(10) = 1001 1001 1000 1111 1101 1010 0010 1110(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 2 576 341 550(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in one's complement representation:
2 576 341 550(10) = 0000 0000 0000 0000 0000 0000 0000 0000 1001 1001 1000 1111 1101 1010 0010 1110
Spaces were used to group digits: for binary, by 4, for decimal, by 3.