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;
- 1 299 934 954 ÷ 2 = 649 967 477 + 0;
- 649 967 477 ÷ 2 = 324 983 738 + 1;
- 324 983 738 ÷ 2 = 162 491 869 + 0;
- 162 491 869 ÷ 2 = 81 245 934 + 1;
- 81 245 934 ÷ 2 = 40 622 967 + 0;
- 40 622 967 ÷ 2 = 20 311 483 + 1;
- 20 311 483 ÷ 2 = 10 155 741 + 1;
- 10 155 741 ÷ 2 = 5 077 870 + 1;
- 5 077 870 ÷ 2 = 2 538 935 + 0;
- 2 538 935 ÷ 2 = 1 269 467 + 1;
- 1 269 467 ÷ 2 = 634 733 + 1;
- 634 733 ÷ 2 = 317 366 + 1;
- 317 366 ÷ 2 = 158 683 + 0;
- 158 683 ÷ 2 = 79 341 + 1;
- 79 341 ÷ 2 = 39 670 + 1;
- 39 670 ÷ 2 = 19 835 + 0;
- 19 835 ÷ 2 = 9 917 + 1;
- 9 917 ÷ 2 = 4 958 + 1;
- 4 958 ÷ 2 = 2 479 + 0;
- 2 479 ÷ 2 = 1 239 + 1;
- 1 239 ÷ 2 = 619 + 1;
- 619 ÷ 2 = 309 + 1;
- 309 ÷ 2 = 154 + 1;
- 154 ÷ 2 = 77 + 0;
- 77 ÷ 2 = 38 + 1;
- 38 ÷ 2 = 19 + 0;
- 19 ÷ 2 = 9 + 1;
- 9 ÷ 2 = 4 + 1;
- 4 ÷ 2 = 2 + 0;
- 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.
1 299 934 954(10) = 100 1101 0111 1011 0110 1110 1110 1010(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:
1 299 934 954(10) = 0100 1101 0111 1011 0110 1110 1110 1010
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 -1 299 934 954(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-1 299 934 954(10) = 1100 1101 0111 1011 0110 1110 1110 1010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.