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;
- 306 606 127 ÷ 2 = 153 303 063 + 1;
- 153 303 063 ÷ 2 = 76 651 531 + 1;
- 76 651 531 ÷ 2 = 38 325 765 + 1;
- 38 325 765 ÷ 2 = 19 162 882 + 1;
- 19 162 882 ÷ 2 = 9 581 441 + 0;
- 9 581 441 ÷ 2 = 4 790 720 + 1;
- 4 790 720 ÷ 2 = 2 395 360 + 0;
- 2 395 360 ÷ 2 = 1 197 680 + 0;
- 1 197 680 ÷ 2 = 598 840 + 0;
- 598 840 ÷ 2 = 299 420 + 0;
- 299 420 ÷ 2 = 149 710 + 0;
- 149 710 ÷ 2 = 74 855 + 0;
- 74 855 ÷ 2 = 37 427 + 1;
- 37 427 ÷ 2 = 18 713 + 1;
- 18 713 ÷ 2 = 9 356 + 1;
- 9 356 ÷ 2 = 4 678 + 0;
- 4 678 ÷ 2 = 2 339 + 0;
- 2 339 ÷ 2 = 1 169 + 1;
- 1 169 ÷ 2 = 584 + 1;
- 584 ÷ 2 = 292 + 0;
- 292 ÷ 2 = 146 + 0;
- 146 ÷ 2 = 73 + 0;
- 73 ÷ 2 = 36 + 1;
- 36 ÷ 2 = 18 + 0;
- 18 ÷ 2 = 9 + 0;
- 9 ÷ 2 = 4 + 1;
- 4 ÷ 2 = 2 + 0;
- 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.
306 606 127(10) = 1 0010 0100 0110 0111 0000 0010 1111(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 29.
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, 29,
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.
306 606 127(10) = 0001 0010 0100 0110 0111 0000 0010 1111
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.
-306 606 127(10) = !(0001 0010 0100 0110 0111 0000 0010 1111)
Number -306 606 127(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:
-306 606 127(10) = 1110 1101 1011 1001 1000 1111 1101 0000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.