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;
- 8 560 101 ÷ 2 = 4 280 050 + 1;
- 4 280 050 ÷ 2 = 2 140 025 + 0;
- 2 140 025 ÷ 2 = 1 070 012 + 1;
- 1 070 012 ÷ 2 = 535 006 + 0;
- 535 006 ÷ 2 = 267 503 + 0;
- 267 503 ÷ 2 = 133 751 + 1;
- 133 751 ÷ 2 = 66 875 + 1;
- 66 875 ÷ 2 = 33 437 + 1;
- 33 437 ÷ 2 = 16 718 + 1;
- 16 718 ÷ 2 = 8 359 + 0;
- 8 359 ÷ 2 = 4 179 + 1;
- 4 179 ÷ 2 = 2 089 + 1;
- 2 089 ÷ 2 = 1 044 + 1;
- 1 044 ÷ 2 = 522 + 0;
- 522 ÷ 2 = 261 + 0;
- 261 ÷ 2 = 130 + 1;
- 130 ÷ 2 = 65 + 0;
- 65 ÷ 2 = 32 + 1;
- 32 ÷ 2 = 16 + 0;
- 16 ÷ 2 = 8 + 0;
- 8 ÷ 2 = 4 + 0;
- 4 ÷ 2 = 2 + 0;
- 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.
8 560 101(10) = 1000 0010 1001 1101 1110 0101(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) 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, 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.
8 560 101(10) = 0000 0000 1000 0010 1001 1101 1110 0101
6. Get the negative integer number representation:
To write the negative integer number on 32 bits (4 Bytes),
as a signed binary in one's complement representation,
... replace all the bits on 0 with 1s and all the bits set on 1 with 0s.
Reverse the digits, flip the digits:
Replace the bits set on 0 with 1s and the bits set on 1 with 0s.
-8 560 101(10) = !(0000 0000 1000 0010 1001 1101 1110 0101)
Number -8 560 101(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in one's complement representation:
-8 560 101(10) = 1111 1111 0111 1101 0110 0010 0001 1010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.