1. 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;
- 4 567 831 ÷ 2 = 2 283 915 + 1;
- 2 283 915 ÷ 2 = 1 141 957 + 1;
- 1 141 957 ÷ 2 = 570 978 + 1;
- 570 978 ÷ 2 = 285 489 + 0;
- 285 489 ÷ 2 = 142 744 + 1;
- 142 744 ÷ 2 = 71 372 + 0;
- 71 372 ÷ 2 = 35 686 + 0;
- 35 686 ÷ 2 = 17 843 + 0;
- 17 843 ÷ 2 = 8 921 + 1;
- 8 921 ÷ 2 = 4 460 + 1;
- 4 460 ÷ 2 = 2 230 + 0;
- 2 230 ÷ 2 = 1 115 + 0;
- 1 115 ÷ 2 = 557 + 1;
- 557 ÷ 2 = 278 + 1;
- 278 ÷ 2 = 139 + 0;
- 139 ÷ 2 = 69 + 1;
- 69 ÷ 2 = 34 + 1;
- 34 ÷ 2 = 17 + 0;
- 17 ÷ 2 = 8 + 1;
- 8 ÷ 2 = 4 + 0;
- 4 ÷ 2 = 2 + 0;
- 2 ÷ 2 = 1 + 0;
- 1 ÷ 2 = 0 + 1;
2. Construct the base 2 representation of the positive number:
Take all the remainders starting from the bottom of the list constructed above.
4 567 831(10) = 100 0101 1011 0011 0001 0111(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 23.
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, 23,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 32.
4. 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:
Number 4 567 831(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
4 567 831(10) = 0000 0000 0100 0101 1011 0011 0001 0111
Spaces were used to group digits: for binary, by 4, for decimal, by 3.