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;
- 50 143 ÷ 2 = 25 071 + 1;
- 25 071 ÷ 2 = 12 535 + 1;
- 12 535 ÷ 2 = 6 267 + 1;
- 6 267 ÷ 2 = 3 133 + 1;
- 3 133 ÷ 2 = 1 566 + 1;
- 1 566 ÷ 2 = 783 + 0;
- 783 ÷ 2 = 391 + 1;
- 391 ÷ 2 = 195 + 1;
- 195 ÷ 2 = 97 + 1;
- 97 ÷ 2 = 48 + 1;
- 48 ÷ 2 = 24 + 0;
- 24 ÷ 2 = 12 + 0;
- 12 ÷ 2 = 6 + 0;
- 6 ÷ 2 = 3 + 0;
- 3 ÷ 2 = 1 + 1;
- 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.
50 143(10) = 1100 0011 1101 1111(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 16.
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, 16,
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 50 143(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
50 143(10) = 0000 0000 0000 0000 1100 0011 1101 1111
Spaces were used to group digits: for binary, by 4, for decimal, by 3.