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;
- 173 351 251 ÷ 2 = 86 675 625 + 1;
- 86 675 625 ÷ 2 = 43 337 812 + 1;
- 43 337 812 ÷ 2 = 21 668 906 + 0;
- 21 668 906 ÷ 2 = 10 834 453 + 0;
- 10 834 453 ÷ 2 = 5 417 226 + 1;
- 5 417 226 ÷ 2 = 2 708 613 + 0;
- 2 708 613 ÷ 2 = 1 354 306 + 1;
- 1 354 306 ÷ 2 = 677 153 + 0;
- 677 153 ÷ 2 = 338 576 + 1;
- 338 576 ÷ 2 = 169 288 + 0;
- 169 288 ÷ 2 = 84 644 + 0;
- 84 644 ÷ 2 = 42 322 + 0;
- 42 322 ÷ 2 = 21 161 + 0;
- 21 161 ÷ 2 = 10 580 + 1;
- 10 580 ÷ 2 = 5 290 + 0;
- 5 290 ÷ 2 = 2 645 + 0;
- 2 645 ÷ 2 = 1 322 + 1;
- 1 322 ÷ 2 = 661 + 0;
- 661 ÷ 2 = 330 + 1;
- 330 ÷ 2 = 165 + 0;
- 165 ÷ 2 = 82 + 1;
- 82 ÷ 2 = 41 + 0;
- 41 ÷ 2 = 20 + 1;
- 20 ÷ 2 = 10 + 0;
- 10 ÷ 2 = 5 + 0;
- 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.
173 351 251(10) = 1010 0101 0101 0010 0001 0101 0011(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 28.
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, 28,
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.
173 351 251(10) = 0000 1010 0101 0101 0010 0001 0101 0011
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.
-173 351 251(10) = !(0000 1010 0101 0101 0010 0001 0101 0011)
Number -173 351 251(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:
-173 351 251(10) = 1111 0101 1010 1010 1101 1110 1010 1100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.