1. Start with the positive version of the number:
|-794 412 989| = 794 412 989
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;
- 794 412 989 ÷ 2 = 397 206 494 + 1;
- 397 206 494 ÷ 2 = 198 603 247 + 0;
- 198 603 247 ÷ 2 = 99 301 623 + 1;
- 99 301 623 ÷ 2 = 49 650 811 + 1;
- 49 650 811 ÷ 2 = 24 825 405 + 1;
- 24 825 405 ÷ 2 = 12 412 702 + 1;
- 12 412 702 ÷ 2 = 6 206 351 + 0;
- 6 206 351 ÷ 2 = 3 103 175 + 1;
- 3 103 175 ÷ 2 = 1 551 587 + 1;
- 1 551 587 ÷ 2 = 775 793 + 1;
- 775 793 ÷ 2 = 387 896 + 1;
- 387 896 ÷ 2 = 193 948 + 0;
- 193 948 ÷ 2 = 96 974 + 0;
- 96 974 ÷ 2 = 48 487 + 0;
- 48 487 ÷ 2 = 24 243 + 1;
- 24 243 ÷ 2 = 12 121 + 1;
- 12 121 ÷ 2 = 6 060 + 1;
- 6 060 ÷ 2 = 3 030 + 0;
- 3 030 ÷ 2 = 1 515 + 0;
- 1 515 ÷ 2 = 757 + 1;
- 757 ÷ 2 = 378 + 1;
- 378 ÷ 2 = 189 + 0;
- 189 ÷ 2 = 94 + 1;
- 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.
794 412 989(10) = 10 1111 0101 1001 1100 0111 1011 1101(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) indicates 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.
794 412 989(10) = 0010 1111 0101 1001 1100 0111 1011 1101
6. Get the negative integer number representation:
To write the negative integer number on 32 bits (4 Bytes),
as a signed binary in one's complement representation,
... replace all the bits on 0 with 1s and all the bits set on 1 with 0s.
Reverse the digits, flip the digits:
Replace the bits set on 0 with 1s and the bits set on 1 with 0s.
-794 412 989(10) = !(0010 1111 0101 1001 1100 0111 1011 1101)
Number -794 412 989(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in one's complement representation:
-794 412 989(10) = 1101 0000 1010 0110 0011 1000 0100 0010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.