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;
- 9 333 839 ÷ 2 = 4 666 919 + 1;
- 4 666 919 ÷ 2 = 2 333 459 + 1;
- 2 333 459 ÷ 2 = 1 166 729 + 1;
- 1 166 729 ÷ 2 = 583 364 + 1;
- 583 364 ÷ 2 = 291 682 + 0;
- 291 682 ÷ 2 = 145 841 + 0;
- 145 841 ÷ 2 = 72 920 + 1;
- 72 920 ÷ 2 = 36 460 + 0;
- 36 460 ÷ 2 = 18 230 + 0;
- 18 230 ÷ 2 = 9 115 + 0;
- 9 115 ÷ 2 = 4 557 + 1;
- 4 557 ÷ 2 = 2 278 + 1;
- 2 278 ÷ 2 = 1 139 + 0;
- 1 139 ÷ 2 = 569 + 1;
- 569 ÷ 2 = 284 + 1;
- 284 ÷ 2 = 142 + 0;
- 142 ÷ 2 = 71 + 0;
- 71 ÷ 2 = 35 + 1;
- 35 ÷ 2 = 17 + 1;
- 17 ÷ 2 = 8 + 1;
- 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.
9 333 839(10) = 1000 1110 0110 1100 0100 1111(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.
9 333 839(10) = 0000 0000 1000 1110 0110 1100 0100 1111
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.
-9 333 839(10) = !(0000 0000 1000 1110 0110 1100 0100 1111)
Number -9 333 839(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:
-9 333 839(10) = 1111 1111 0111 0001 1001 0011 1011 0000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.