1. Start with the positive version of the number:
|-177 555| = 177 555
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;
- 177 555 ÷ 2 = 88 777 + 1;
- 88 777 ÷ 2 = 44 388 + 1;
- 44 388 ÷ 2 = 22 194 + 0;
- 22 194 ÷ 2 = 11 097 + 0;
- 11 097 ÷ 2 = 5 548 + 1;
- 5 548 ÷ 2 = 2 774 + 0;
- 2 774 ÷ 2 = 1 387 + 0;
- 1 387 ÷ 2 = 693 + 1;
- 693 ÷ 2 = 346 + 1;
- 346 ÷ 2 = 173 + 0;
- 173 ÷ 2 = 86 + 1;
- 86 ÷ 2 = 43 + 0;
- 43 ÷ 2 = 21 + 1;
- 21 ÷ 2 = 10 + 1;
- 10 ÷ 2 = 5 + 0;
- 5 ÷ 2 = 2 + 1;
- 2 ÷ 2 = 1 + 0;
- 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.
177 555(10) = 10 1011 0101 1001 0011(2)
4. 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) 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, 18,
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:
177 555(10) = 0000 0000 0000 0010 1011 0101 1001 0011
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 -177 555(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-177 555(10) = 1000 0000 0000 0010 1011 0101 1001 0011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.