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;
- 10 994 777 ÷ 2 = 5 497 388 + 1;
- 5 497 388 ÷ 2 = 2 748 694 + 0;
- 2 748 694 ÷ 2 = 1 374 347 + 0;
- 1 374 347 ÷ 2 = 687 173 + 1;
- 687 173 ÷ 2 = 343 586 + 1;
- 343 586 ÷ 2 = 171 793 + 0;
- 171 793 ÷ 2 = 85 896 + 1;
- 85 896 ÷ 2 = 42 948 + 0;
- 42 948 ÷ 2 = 21 474 + 0;
- 21 474 ÷ 2 = 10 737 + 0;
- 10 737 ÷ 2 = 5 368 + 1;
- 5 368 ÷ 2 = 2 684 + 0;
- 2 684 ÷ 2 = 1 342 + 0;
- 1 342 ÷ 2 = 671 + 0;
- 671 ÷ 2 = 335 + 1;
- 335 ÷ 2 = 167 + 1;
- 167 ÷ 2 = 83 + 1;
- 83 ÷ 2 = 41 + 1;
- 41 ÷ 2 = 20 + 1;
- 20 ÷ 2 = 10 + 0;
- 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.
10 994 777(10) = 1010 0111 1100 0100 0101 1001(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 24.
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, 24,
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:
10 994 777(10) = 0000 0000 1010 0111 1100 0100 0101 1001
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 -10 994 777(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-10 994 777(10) = 1000 0000 1010 0111 1100 0100 0101 1001
Spaces were used to group digits: for binary, by 4, for decimal, by 3.