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;
- 858 993 425 ÷ 2 = 429 496 712 + 1;
- 429 496 712 ÷ 2 = 214 748 356 + 0;
- 214 748 356 ÷ 2 = 107 374 178 + 0;
- 107 374 178 ÷ 2 = 53 687 089 + 0;
- 53 687 089 ÷ 2 = 26 843 544 + 1;
- 26 843 544 ÷ 2 = 13 421 772 + 0;
- 13 421 772 ÷ 2 = 6 710 886 + 0;
- 6 710 886 ÷ 2 = 3 355 443 + 0;
- 3 355 443 ÷ 2 = 1 677 721 + 1;
- 1 677 721 ÷ 2 = 838 860 + 1;
- 838 860 ÷ 2 = 419 430 + 0;
- 419 430 ÷ 2 = 209 715 + 0;
- 209 715 ÷ 2 = 104 857 + 1;
- 104 857 ÷ 2 = 52 428 + 1;
- 52 428 ÷ 2 = 26 214 + 0;
- 26 214 ÷ 2 = 13 107 + 0;
- 13 107 ÷ 2 = 6 553 + 1;
- 6 553 ÷ 2 = 3 276 + 1;
- 3 276 ÷ 2 = 1 638 + 0;
- 1 638 ÷ 2 = 819 + 0;
- 819 ÷ 2 = 409 + 1;
- 409 ÷ 2 = 204 + 1;
- 204 ÷ 2 = 102 + 0;
- 102 ÷ 2 = 51 + 0;
- 51 ÷ 2 = 25 + 1;
- 25 ÷ 2 = 12 + 1;
- 12 ÷ 2 = 6 + 0;
- 6 ÷ 2 = 3 + 0;
- 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.
858 993 425(10) = 11 0011 0011 0011 0011 0011 0001 0001(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 30.
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, 30,
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:
858 993 425(10) = 0011 0011 0011 0011 0011 0011 0001 0001
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 -858 993 425(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-858 993 425(10) = 1011 0011 0011 0011 0011 0011 0001 0001
Spaces were used to group digits: for binary, by 4, for decimal, by 3.