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;
- 1 036 831 863 ÷ 2 = 518 415 931 + 1;
- 518 415 931 ÷ 2 = 259 207 965 + 1;
- 259 207 965 ÷ 2 = 129 603 982 + 1;
- 129 603 982 ÷ 2 = 64 801 991 + 0;
- 64 801 991 ÷ 2 = 32 400 995 + 1;
- 32 400 995 ÷ 2 = 16 200 497 + 1;
- 16 200 497 ÷ 2 = 8 100 248 + 1;
- 8 100 248 ÷ 2 = 4 050 124 + 0;
- 4 050 124 ÷ 2 = 2 025 062 + 0;
- 2 025 062 ÷ 2 = 1 012 531 + 0;
- 1 012 531 ÷ 2 = 506 265 + 1;
- 506 265 ÷ 2 = 253 132 + 1;
- 253 132 ÷ 2 = 126 566 + 0;
- 126 566 ÷ 2 = 63 283 + 0;
- 63 283 ÷ 2 = 31 641 + 1;
- 31 641 ÷ 2 = 15 820 + 1;
- 15 820 ÷ 2 = 7 910 + 0;
- 7 910 ÷ 2 = 3 955 + 0;
- 3 955 ÷ 2 = 1 977 + 1;
- 1 977 ÷ 2 = 988 + 1;
- 988 ÷ 2 = 494 + 0;
- 494 ÷ 2 = 247 + 0;
- 247 ÷ 2 = 123 + 1;
- 123 ÷ 2 = 61 + 1;
- 61 ÷ 2 = 30 + 1;
- 30 ÷ 2 = 15 + 0;
- 15 ÷ 2 = 7 + 1;
- 7 ÷ 2 = 3 + 1;
- 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.
1 036 831 863(10) = 11 1101 1100 1100 1100 1100 0111 0111(2)
3. 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) 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, 30,
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 1 036 831 863(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:
1 036 831 863(10) = 0011 1101 1100 1100 1100 1100 0111 0111
Spaces were used to group digits: for binary, by 4, for decimal, by 3.