1. Start with the positive version of the number:
|-65 150| = 65 150
2. 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;
- 65 150 ÷ 2 = 32 575 + 0;
- 32 575 ÷ 2 = 16 287 + 1;
- 16 287 ÷ 2 = 8 143 + 1;
- 8 143 ÷ 2 = 4 071 + 1;
- 4 071 ÷ 2 = 2 035 + 1;
- 2 035 ÷ 2 = 1 017 + 1;
- 1 017 ÷ 2 = 508 + 1;
- 508 ÷ 2 = 254 + 0;
- 254 ÷ 2 = 127 + 0;
- 127 ÷ 2 = 63 + 1;
- 63 ÷ 2 = 31 + 1;
- 31 ÷ 2 = 15 + 1;
- 15 ÷ 2 = 7 + 1;
- 7 ÷ 2 = 3 + 1;
- 3 ÷ 2 = 1 + 1;
- 1 ÷ 2 = 0 + 1;
3. Construct the base 2 representation of the positive number:
Take all the remainders starting from the bottom of the list constructed above.
65 150(10) = 1111 1110 0111 1110(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 16.
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, 16,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 32.
5. 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:
65 150(10) = 0000 0000 0000 0000 1111 1110 0111 1110
6. Get the negative integer number representation:
To get the negative integer number representation on 32 bits (4 Bytes),
... change the first bit (the leftmost), from 0 to 1...
Number -65 150(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-65 150(10) = 1000 0000 0000 0000 1111 1110 0111 1110
Spaces were used to group digits: for binary, by 4, for decimal, by 3.