1. Start with the positive version of the number:
|-805 377 142| = 805 377 142
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;
- 805 377 142 ÷ 2 = 402 688 571 + 0;
- 402 688 571 ÷ 2 = 201 344 285 + 1;
- 201 344 285 ÷ 2 = 100 672 142 + 1;
- 100 672 142 ÷ 2 = 50 336 071 + 0;
- 50 336 071 ÷ 2 = 25 168 035 + 1;
- 25 168 035 ÷ 2 = 12 584 017 + 1;
- 12 584 017 ÷ 2 = 6 292 008 + 1;
- 6 292 008 ÷ 2 = 3 146 004 + 0;
- 3 146 004 ÷ 2 = 1 573 002 + 0;
- 1 573 002 ÷ 2 = 786 501 + 0;
- 786 501 ÷ 2 = 393 250 + 1;
- 393 250 ÷ 2 = 196 625 + 0;
- 196 625 ÷ 2 = 98 312 + 1;
- 98 312 ÷ 2 = 49 156 + 0;
- 49 156 ÷ 2 = 24 578 + 0;
- 24 578 ÷ 2 = 12 289 + 0;
- 12 289 ÷ 2 = 6 144 + 1;
- 6 144 ÷ 2 = 3 072 + 0;
- 3 072 ÷ 2 = 1 536 + 0;
- 1 536 ÷ 2 = 768 + 0;
- 768 ÷ 2 = 384 + 0;
- 384 ÷ 2 = 192 + 0;
- 192 ÷ 2 = 96 + 0;
- 96 ÷ 2 = 48 + 0;
- 48 ÷ 2 = 24 + 0;
- 24 ÷ 2 = 12 + 0;
- 12 ÷ 2 = 6 + 0;
- 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.
805 377 142(10) = 11 0000 0000 0001 0001 0100 0111 0110(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:
805 377 142(10) = 0011 0000 0000 0001 0001 0100 0111 0110
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 -805 377 142(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-805 377 142(10) = 1011 0000 0000 0001 0001 0100 0111 0110
Spaces were used to group digits: for binary, by 4, for decimal, by 3.