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;
- 2 033 506 989 ÷ 2 = 1 016 753 494 + 1;
- 1 016 753 494 ÷ 2 = 508 376 747 + 0;
- 508 376 747 ÷ 2 = 254 188 373 + 1;
- 254 188 373 ÷ 2 = 127 094 186 + 1;
- 127 094 186 ÷ 2 = 63 547 093 + 0;
- 63 547 093 ÷ 2 = 31 773 546 + 1;
- 31 773 546 ÷ 2 = 15 886 773 + 0;
- 15 886 773 ÷ 2 = 7 943 386 + 1;
- 7 943 386 ÷ 2 = 3 971 693 + 0;
- 3 971 693 ÷ 2 = 1 985 846 + 1;
- 1 985 846 ÷ 2 = 992 923 + 0;
- 992 923 ÷ 2 = 496 461 + 1;
- 496 461 ÷ 2 = 248 230 + 1;
- 248 230 ÷ 2 = 124 115 + 0;
- 124 115 ÷ 2 = 62 057 + 1;
- 62 057 ÷ 2 = 31 028 + 1;
- 31 028 ÷ 2 = 15 514 + 0;
- 15 514 ÷ 2 = 7 757 + 0;
- 7 757 ÷ 2 = 3 878 + 1;
- 3 878 ÷ 2 = 1 939 + 0;
- 1 939 ÷ 2 = 969 + 1;
- 969 ÷ 2 = 484 + 1;
- 484 ÷ 2 = 242 + 0;
- 242 ÷ 2 = 121 + 0;
- 121 ÷ 2 = 60 + 1;
- 60 ÷ 2 = 30 + 0;
- 30 ÷ 2 = 15 + 0;
- 15 ÷ 2 = 7 + 1;
- 7 ÷ 2 = 3 + 1;
- 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.
2 033 506 989(10) = 111 1001 0011 0100 1101 1010 1010 1101(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 31.
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, 31,
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.
2 033 506 989(10) = 0111 1001 0011 0100 1101 1010 1010 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.
-2 033 506 989(10) = !(0111 1001 0011 0100 1101 1010 1010 1101)
Number -2 033 506 989(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:
-2 033 506 989(10) = 1000 0110 1100 1011 0010 0101 0101 0010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.