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;
- 980 041 ÷ 2 = 490 020 + 1;
- 490 020 ÷ 2 = 245 010 + 0;
- 245 010 ÷ 2 = 122 505 + 0;
- 122 505 ÷ 2 = 61 252 + 1;
- 61 252 ÷ 2 = 30 626 + 0;
- 30 626 ÷ 2 = 15 313 + 0;
- 15 313 ÷ 2 = 7 656 + 1;
- 7 656 ÷ 2 = 3 828 + 0;
- 3 828 ÷ 2 = 1 914 + 0;
- 1 914 ÷ 2 = 957 + 0;
- 957 ÷ 2 = 478 + 1;
- 478 ÷ 2 = 239 + 0;
- 239 ÷ 2 = 119 + 1;
- 119 ÷ 2 = 59 + 1;
- 59 ÷ 2 = 29 + 1;
- 29 ÷ 2 = 14 + 1;
- 14 ÷ 2 = 7 + 0;
- 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.
980 041(10) = 1110 1111 0100 0100 1001(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 20.
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, 20,
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 980 041(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:
980 041(10) = 0000 0000 0000 1110 1111 0100 0100 1001
Spaces were used to group digits: for binary, by 4, for decimal, by 3.