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;
- 1 482 850 895 ÷ 2 = 741 425 447 + 1;
- 741 425 447 ÷ 2 = 370 712 723 + 1;
- 370 712 723 ÷ 2 = 185 356 361 + 1;
- 185 356 361 ÷ 2 = 92 678 180 + 1;
- 92 678 180 ÷ 2 = 46 339 090 + 0;
- 46 339 090 ÷ 2 = 23 169 545 + 0;
- 23 169 545 ÷ 2 = 11 584 772 + 1;
- 11 584 772 ÷ 2 = 5 792 386 + 0;
- 5 792 386 ÷ 2 = 2 896 193 + 0;
- 2 896 193 ÷ 2 = 1 448 096 + 1;
- 1 448 096 ÷ 2 = 724 048 + 0;
- 724 048 ÷ 2 = 362 024 + 0;
- 362 024 ÷ 2 = 181 012 + 0;
- 181 012 ÷ 2 = 90 506 + 0;
- 90 506 ÷ 2 = 45 253 + 0;
- 45 253 ÷ 2 = 22 626 + 1;
- 22 626 ÷ 2 = 11 313 + 0;
- 11 313 ÷ 2 = 5 656 + 1;
- 5 656 ÷ 2 = 2 828 + 0;
- 2 828 ÷ 2 = 1 414 + 0;
- 1 414 ÷ 2 = 707 + 0;
- 707 ÷ 2 = 353 + 1;
- 353 ÷ 2 = 176 + 1;
- 176 ÷ 2 = 88 + 0;
- 88 ÷ 2 = 44 + 0;
- 44 ÷ 2 = 22 + 0;
- 22 ÷ 2 = 11 + 0;
- 11 ÷ 2 = 5 + 1;
- 5 ÷ 2 = 2 + 1;
- 2 ÷ 2 = 1 + 0;
- 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.
1 482 850 895(10) = 101 1000 0110 0010 1000 0010 0100 1111(2)
4. 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) 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, 31,
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:
1 482 850 895(10) = 0101 1000 0110 0010 1000 0010 0100 1111
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 -1 482 850 895(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-1 482 850 895(10) = 1101 1000 0110 0010 1000 0010 0100 1111
Spaces were used to group digits: for binary, by 4, for decimal, by 3.