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;
- 11 109 901 ÷ 2 = 5 554 950 + 1;
- 5 554 950 ÷ 2 = 2 777 475 + 0;
- 2 777 475 ÷ 2 = 1 388 737 + 1;
- 1 388 737 ÷ 2 = 694 368 + 1;
- 694 368 ÷ 2 = 347 184 + 0;
- 347 184 ÷ 2 = 173 592 + 0;
- 173 592 ÷ 2 = 86 796 + 0;
- 86 796 ÷ 2 = 43 398 + 0;
- 43 398 ÷ 2 = 21 699 + 0;
- 21 699 ÷ 2 = 10 849 + 1;
- 10 849 ÷ 2 = 5 424 + 1;
- 5 424 ÷ 2 = 2 712 + 0;
- 2 712 ÷ 2 = 1 356 + 0;
- 1 356 ÷ 2 = 678 + 0;
- 678 ÷ 2 = 339 + 0;
- 339 ÷ 2 = 169 + 1;
- 169 ÷ 2 = 84 + 1;
- 84 ÷ 2 = 42 + 0;
- 42 ÷ 2 = 21 + 0;
- 21 ÷ 2 = 10 + 1;
- 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.
11 109 901(10) = 1010 1001 1000 0110 0000 1101(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) 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, 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.
11 109 901(10) = 0000 0000 1010 1001 1000 0110 0000 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.
-11 109 901(10) = !(0000 0000 1010 1001 1000 0110 0000 1101)
Number -11 109 901(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:
-11 109 901(10) = 1111 1111 0101 0110 0111 1001 1111 0010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.