1. Start with the positive version of the number:
|-939 524 069| = 939 524 069
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;
- 939 524 069 ÷ 2 = 469 762 034 + 1;
- 469 762 034 ÷ 2 = 234 881 017 + 0;
- 234 881 017 ÷ 2 = 117 440 508 + 1;
- 117 440 508 ÷ 2 = 58 720 254 + 0;
- 58 720 254 ÷ 2 = 29 360 127 + 0;
- 29 360 127 ÷ 2 = 14 680 063 + 1;
- 14 680 063 ÷ 2 = 7 340 031 + 1;
- 7 340 031 ÷ 2 = 3 670 015 + 1;
- 3 670 015 ÷ 2 = 1 835 007 + 1;
- 1 835 007 ÷ 2 = 917 503 + 1;
- 917 503 ÷ 2 = 458 751 + 1;
- 458 751 ÷ 2 = 229 375 + 1;
- 229 375 ÷ 2 = 114 687 + 1;
- 114 687 ÷ 2 = 57 343 + 1;
- 57 343 ÷ 2 = 28 671 + 1;
- 28 671 ÷ 2 = 14 335 + 1;
- 14 335 ÷ 2 = 7 167 + 1;
- 7 167 ÷ 2 = 3 583 + 1;
- 3 583 ÷ 2 = 1 791 + 1;
- 1 791 ÷ 2 = 895 + 1;
- 895 ÷ 2 = 447 + 1;
- 447 ÷ 2 = 223 + 1;
- 223 ÷ 2 = 111 + 1;
- 111 ÷ 2 = 55 + 1;
- 55 ÷ 2 = 27 + 1;
- 27 ÷ 2 = 13 + 1;
- 13 ÷ 2 = 6 + 1;
- 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.
939 524 069(10) = 11 0111 1111 1111 1111 1111 1110 0101(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:
939 524 069(10) = 0011 0111 1111 1111 1111 1111 1110 0101
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 -939 524 069(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-939 524 069(10) = 1011 0111 1111 1111 1111 1111 1110 0101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.