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;
- 295 094 222 ÷ 2 = 147 547 111 + 0;
- 147 547 111 ÷ 2 = 73 773 555 + 1;
- 73 773 555 ÷ 2 = 36 886 777 + 1;
- 36 886 777 ÷ 2 = 18 443 388 + 1;
- 18 443 388 ÷ 2 = 9 221 694 + 0;
- 9 221 694 ÷ 2 = 4 610 847 + 0;
- 4 610 847 ÷ 2 = 2 305 423 + 1;
- 2 305 423 ÷ 2 = 1 152 711 + 1;
- 1 152 711 ÷ 2 = 576 355 + 1;
- 576 355 ÷ 2 = 288 177 + 1;
- 288 177 ÷ 2 = 144 088 + 1;
- 144 088 ÷ 2 = 72 044 + 0;
- 72 044 ÷ 2 = 36 022 + 0;
- 36 022 ÷ 2 = 18 011 + 0;
- 18 011 ÷ 2 = 9 005 + 1;
- 9 005 ÷ 2 = 4 502 + 1;
- 4 502 ÷ 2 = 2 251 + 0;
- 2 251 ÷ 2 = 1 125 + 1;
- 1 125 ÷ 2 = 562 + 1;
- 562 ÷ 2 = 281 + 0;
- 281 ÷ 2 = 140 + 1;
- 140 ÷ 2 = 70 + 0;
- 70 ÷ 2 = 35 + 0;
- 35 ÷ 2 = 17 + 1;
- 17 ÷ 2 = 8 + 1;
- 8 ÷ 2 = 4 + 0;
- 4 ÷ 2 = 2 + 0;
- 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.
295 094 222(10) = 1 0001 1001 0110 1100 0111 1100 1110(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 29.
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, 29,
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 295 094 222(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in two's complement representation:
295 094 222(10) = 0001 0001 1001 0110 1100 0111 1100 1110
Spaces were used to group digits: for binary, by 4, for decimal, by 3.