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;
- 975 308 467 ÷ 2 = 487 654 233 + 1;
- 487 654 233 ÷ 2 = 243 827 116 + 1;
- 243 827 116 ÷ 2 = 121 913 558 + 0;
- 121 913 558 ÷ 2 = 60 956 779 + 0;
- 60 956 779 ÷ 2 = 30 478 389 + 1;
- 30 478 389 ÷ 2 = 15 239 194 + 1;
- 15 239 194 ÷ 2 = 7 619 597 + 0;
- 7 619 597 ÷ 2 = 3 809 798 + 1;
- 3 809 798 ÷ 2 = 1 904 899 + 0;
- 1 904 899 ÷ 2 = 952 449 + 1;
- 952 449 ÷ 2 = 476 224 + 1;
- 476 224 ÷ 2 = 238 112 + 0;
- 238 112 ÷ 2 = 119 056 + 0;
- 119 056 ÷ 2 = 59 528 + 0;
- 59 528 ÷ 2 = 29 764 + 0;
- 29 764 ÷ 2 = 14 882 + 0;
- 14 882 ÷ 2 = 7 441 + 0;
- 7 441 ÷ 2 = 3 720 + 1;
- 3 720 ÷ 2 = 1 860 + 0;
- 1 860 ÷ 2 = 930 + 0;
- 930 ÷ 2 = 465 + 0;
- 465 ÷ 2 = 232 + 1;
- 232 ÷ 2 = 116 + 0;
- 116 ÷ 2 = 58 + 0;
- 58 ÷ 2 = 29 + 0;
- 29 ÷ 2 = 14 + 1;
- 14 ÷ 2 = 7 + 0;
- 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.
975 308 467(10) = 11 1010 0010 0010 0000 0110 1011 0011(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 30.
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, 30,
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:
975 308 467(10) = 0011 1010 0010 0010 0000 0110 1011 0011
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 -975 308 467(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-975 308 467(10) = 1011 1010 0010 0010 0000 0110 1011 0011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.