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;
- 378 798 ÷ 2 = 189 399 + 0;
- 189 399 ÷ 2 = 94 699 + 1;
- 94 699 ÷ 2 = 47 349 + 1;
- 47 349 ÷ 2 = 23 674 + 1;
- 23 674 ÷ 2 = 11 837 + 0;
- 11 837 ÷ 2 = 5 918 + 1;
- 5 918 ÷ 2 = 2 959 + 0;
- 2 959 ÷ 2 = 1 479 + 1;
- 1 479 ÷ 2 = 739 + 1;
- 739 ÷ 2 = 369 + 1;
- 369 ÷ 2 = 184 + 1;
- 184 ÷ 2 = 92 + 0;
- 92 ÷ 2 = 46 + 0;
- 46 ÷ 2 = 23 + 0;
- 23 ÷ 2 = 11 + 1;
- 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.
378 798(10) = 101 1100 0111 1010 1110(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) is reserved for 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 378 798(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
378 798(10) = 0000 0000 0000 0101 1100 0111 1010 1110
Spaces were used to group digits: for binary, by 4, for decimal, by 3.