1. Start with the positive version of the number:
|-12 345 765| = 12 345 765
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;
- 12 345 765 ÷ 2 = 6 172 882 + 1;
- 6 172 882 ÷ 2 = 3 086 441 + 0;
- 3 086 441 ÷ 2 = 1 543 220 + 1;
- 1 543 220 ÷ 2 = 771 610 + 0;
- 771 610 ÷ 2 = 385 805 + 0;
- 385 805 ÷ 2 = 192 902 + 1;
- 192 902 ÷ 2 = 96 451 + 0;
- 96 451 ÷ 2 = 48 225 + 1;
- 48 225 ÷ 2 = 24 112 + 1;
- 24 112 ÷ 2 = 12 056 + 0;
- 12 056 ÷ 2 = 6 028 + 0;
- 6 028 ÷ 2 = 3 014 + 0;
- 3 014 ÷ 2 = 1 507 + 0;
- 1 507 ÷ 2 = 753 + 1;
- 753 ÷ 2 = 376 + 1;
- 376 ÷ 2 = 188 + 0;
- 188 ÷ 2 = 94 + 0;
- 94 ÷ 2 = 47 + 0;
- 47 ÷ 2 = 23 + 1;
- 23 ÷ 2 = 11 + 1;
- 11 ÷ 2 = 5 + 1;
- 5 ÷ 2 = 2 + 1;
- 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.
12 345 765(10) = 1011 1100 0110 0001 1010 0101(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 24.
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, 24,
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:
12 345 765(10) = 0000 0000 1011 1100 0110 0001 1010 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 -12 345 765(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-12 345 765(10) = 1000 0000 1011 1100 0110 0001 1010 0101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.