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;
- 31 504 ÷ 2 = 15 752 + 0;
- 15 752 ÷ 2 = 7 876 + 0;
- 7 876 ÷ 2 = 3 938 + 0;
- 3 938 ÷ 2 = 1 969 + 0;
- 1 969 ÷ 2 = 984 + 1;
- 984 ÷ 2 = 492 + 0;
- 492 ÷ 2 = 246 + 0;
- 246 ÷ 2 = 123 + 0;
- 123 ÷ 2 = 61 + 1;
- 61 ÷ 2 = 30 + 1;
- 30 ÷ 2 = 15 + 0;
- 15 ÷ 2 = 7 + 1;
- 7 ÷ 2 = 3 + 1;
- 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.
31 504(10) = 111 1011 0001 0000(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 15.
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, 15,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 16.
4. Get the positive binary computer representation on 16 bits (2 Bytes):
If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 16.
Number 31 504(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:
Spaces were used to group digits: for binary, by 4, for decimal, by 3.