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;
- 2 033 506 857 ÷ 2 = 1 016 753 428 + 1;
- 1 016 753 428 ÷ 2 = 508 376 714 + 0;
- 508 376 714 ÷ 2 = 254 188 357 + 0;
- 254 188 357 ÷ 2 = 127 094 178 + 1;
- 127 094 178 ÷ 2 = 63 547 089 + 0;
- 63 547 089 ÷ 2 = 31 773 544 + 1;
- 31 773 544 ÷ 2 = 15 886 772 + 0;
- 15 886 772 ÷ 2 = 7 943 386 + 0;
- 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.
2 033 506 857(10) = 111 1001 0011 0100 1101 1010 0010 1001(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) is reserved for 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:
2 033 506 857(10) = 0111 1001 0011 0100 1101 1010 0010 1001
6. Get the negative integer number representation:
To get the negative integer number representation on 32 bits (4 Bytes),
... change the first bit (the leftmost), from 0 to 1...
Number -2 033 506 857(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-2 033 506 857(10) = 1111 1001 0011 0100 1101 1010 0010 1001
Spaces were used to group digits: for binary, by 4, for decimal, by 3.