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;
- 255 127 ÷ 2 = 127 563 + 1;
- 127 563 ÷ 2 = 63 781 + 1;
- 63 781 ÷ 2 = 31 890 + 1;
- 31 890 ÷ 2 = 15 945 + 0;
- 15 945 ÷ 2 = 7 972 + 1;
- 7 972 ÷ 2 = 3 986 + 0;
- 3 986 ÷ 2 = 1 993 + 0;
- 1 993 ÷ 2 = 996 + 1;
- 996 ÷ 2 = 498 + 0;
- 498 ÷ 2 = 249 + 0;
- 249 ÷ 2 = 124 + 1;
- 124 ÷ 2 = 62 + 0;
- 62 ÷ 2 = 31 + 0;
- 31 ÷ 2 = 15 + 1;
- 15 ÷ 2 = 7 + 1;
- 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.
255 127(10) = 11 1110 0100 1001 0111(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 18.
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, 18,
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 255 127(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:
255 127(10) = 0000 0000 0000 0011 1110 0100 1001 0111
Spaces were used to group digits: for binary, by 4, for decimal, by 3.