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;
- 656 618 ÷ 2 = 328 309 + 0;
- 328 309 ÷ 2 = 164 154 + 1;
- 164 154 ÷ 2 = 82 077 + 0;
- 82 077 ÷ 2 = 41 038 + 1;
- 41 038 ÷ 2 = 20 519 + 0;
- 20 519 ÷ 2 = 10 259 + 1;
- 10 259 ÷ 2 = 5 129 + 1;
- 5 129 ÷ 2 = 2 564 + 1;
- 2 564 ÷ 2 = 1 282 + 0;
- 1 282 ÷ 2 = 641 + 0;
- 641 ÷ 2 = 320 + 1;
- 320 ÷ 2 = 160 + 0;
- 160 ÷ 2 = 80 + 0;
- 80 ÷ 2 = 40 + 0;
- 40 ÷ 2 = 20 + 0;
- 20 ÷ 2 = 10 + 0;
- 10 ÷ 2 = 5 + 0;
- 5 ÷ 2 = 2 + 1;
- 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.
656 618(10) = 1010 0000 0100 1110 1010(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 656 618(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:
656 618(10) = 0000 0000 0000 1010 0000 0100 1110 1010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.