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;
- 369 692 ÷ 2 = 184 846 + 0;
- 184 846 ÷ 2 = 92 423 + 0;
- 92 423 ÷ 2 = 46 211 + 1;
- 46 211 ÷ 2 = 23 105 + 1;
- 23 105 ÷ 2 = 11 552 + 1;
- 11 552 ÷ 2 = 5 776 + 0;
- 5 776 ÷ 2 = 2 888 + 0;
- 2 888 ÷ 2 = 1 444 + 0;
- 1 444 ÷ 2 = 722 + 0;
- 722 ÷ 2 = 361 + 0;
- 361 ÷ 2 = 180 + 1;
- 180 ÷ 2 = 90 + 0;
- 90 ÷ 2 = 45 + 0;
- 45 ÷ 2 = 22 + 1;
- 22 ÷ 2 = 11 + 0;
- 11 ÷ 2 = 5 + 1;
- 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.
369 692(10) = 101 1010 0100 0001 1100(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 19.
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, 19,
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 369 692(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:
369 692(10) = 0000 0000 0000 0101 1010 0100 0001 1100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.