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;
- 10 203 040 ÷ 2 = 5 101 520 + 0;
- 5 101 520 ÷ 2 = 2 550 760 + 0;
- 2 550 760 ÷ 2 = 1 275 380 + 0;
- 1 275 380 ÷ 2 = 637 690 + 0;
- 637 690 ÷ 2 = 318 845 + 0;
- 318 845 ÷ 2 = 159 422 + 1;
- 159 422 ÷ 2 = 79 711 + 0;
- 79 711 ÷ 2 = 39 855 + 1;
- 39 855 ÷ 2 = 19 927 + 1;
- 19 927 ÷ 2 = 9 963 + 1;
- 9 963 ÷ 2 = 4 981 + 1;
- 4 981 ÷ 2 = 2 490 + 1;
- 2 490 ÷ 2 = 1 245 + 0;
- 1 245 ÷ 2 = 622 + 1;
- 622 ÷ 2 = 311 + 0;
- 311 ÷ 2 = 155 + 1;
- 155 ÷ 2 = 77 + 1;
- 77 ÷ 2 = 38 + 1;
- 38 ÷ 2 = 19 + 0;
- 19 ÷ 2 = 9 + 1;
- 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.
10 203 040(10) = 1001 1011 1010 1111 1010 0000(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) 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, 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:
10 203 040(10) = 0000 0000 1001 1011 1010 1111 1010 0000
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 -10 203 040(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-10 203 040(10) = 1000 0000 1001 1011 1010 1111 1010 0000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.