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;
- 87 052 ÷ 2 = 43 526 + 0;
- 43 526 ÷ 2 = 21 763 + 0;
- 21 763 ÷ 2 = 10 881 + 1;
- 10 881 ÷ 2 = 5 440 + 1;
- 5 440 ÷ 2 = 2 720 + 0;
- 2 720 ÷ 2 = 1 360 + 0;
- 1 360 ÷ 2 = 680 + 0;
- 680 ÷ 2 = 340 + 0;
- 340 ÷ 2 = 170 + 0;
- 170 ÷ 2 = 85 + 0;
- 85 ÷ 2 = 42 + 1;
- 42 ÷ 2 = 21 + 0;
- 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.
87 052(10) = 1 0101 0100 0000 1100(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.
87 052(10) = 0000 0000 0000 0001 0101 0100 0000 1100
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.
-87 052(10) = !(0000 0000 0000 0001 0101 0100 0000 1100)
Number -87 052(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:
-87 052(10) = 1111 1111 1111 1110 1010 1011 1111 0011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.