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;
- 49 237 ÷ 2 = 24 618 + 1;
- 24 618 ÷ 2 = 12 309 + 0;
- 12 309 ÷ 2 = 6 154 + 1;
- 6 154 ÷ 2 = 3 077 + 0;
- 3 077 ÷ 2 = 1 538 + 1;
- 1 538 ÷ 2 = 769 + 0;
- 769 ÷ 2 = 384 + 1;
- 384 ÷ 2 = 192 + 0;
- 192 ÷ 2 = 96 + 0;
- 96 ÷ 2 = 48 + 0;
- 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.
49 237(10) = 1100 0000 0101 0101(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) indicates 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 49 237(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in one's complement representation:
49 237(10) = 0000 0000 0000 0000 1100 0000 0101 0101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.