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;
- 1 999 987 ÷ 2 = 999 993 + 1;
- 999 993 ÷ 2 = 499 996 + 1;
- 499 996 ÷ 2 = 249 998 + 0;
- 249 998 ÷ 2 = 124 999 + 0;
- 124 999 ÷ 2 = 62 499 + 1;
- 62 499 ÷ 2 = 31 249 + 1;
- 31 249 ÷ 2 = 15 624 + 1;
- 15 624 ÷ 2 = 7 812 + 0;
- 7 812 ÷ 2 = 3 906 + 0;
- 3 906 ÷ 2 = 1 953 + 0;
- 1 953 ÷ 2 = 976 + 1;
- 976 ÷ 2 = 488 + 0;
- 488 ÷ 2 = 244 + 0;
- 244 ÷ 2 = 122 + 0;
- 122 ÷ 2 = 61 + 0;
- 61 ÷ 2 = 30 + 1;
- 30 ÷ 2 = 15 + 0;
- 15 ÷ 2 = 7 + 1;
- 7 ÷ 2 = 3 + 1;
- 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.
1 999 987(10) = 1 1110 1000 0100 0111 0011(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 21.
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, 21,
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:
1 999 987(10) = 0000 0000 0001 1110 1000 0100 0111 0011
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 -1 999 987(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-1 999 987(10) = 1000 0000 0001 1110 1000 0100 0111 0011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.