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;
- 94 903 ÷ 2 = 47 451 + 1;
- 47 451 ÷ 2 = 23 725 + 1;
- 23 725 ÷ 2 = 11 862 + 1;
- 11 862 ÷ 2 = 5 931 + 0;
- 5 931 ÷ 2 = 2 965 + 1;
- 2 965 ÷ 2 = 1 482 + 1;
- 1 482 ÷ 2 = 741 + 0;
- 741 ÷ 2 = 370 + 1;
- 370 ÷ 2 = 185 + 0;
- 185 ÷ 2 = 92 + 1;
- 92 ÷ 2 = 46 + 0;
- 46 ÷ 2 = 23 + 0;
- 23 ÷ 2 = 11 + 1;
- 11 ÷ 2 = 5 + 1;
- 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.
94 903(10) = 1 0111 0010 1011 0111(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 17.
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, 17,
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.
94 903(10) = 0000 0000 0000 0001 0111 0010 1011 0111
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.
-94 903(10) = !(0000 0000 0000 0001 0111 0010 1011 0111)
Number -94 903(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:
-94 903(10) = 1111 1111 1111 1110 1000 1101 0100 1000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.