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;
- 33 456 452 ÷ 2 = 16 728 226 + 0;
- 16 728 226 ÷ 2 = 8 364 113 + 0;
- 8 364 113 ÷ 2 = 4 182 056 + 1;
- 4 182 056 ÷ 2 = 2 091 028 + 0;
- 2 091 028 ÷ 2 = 1 045 514 + 0;
- 1 045 514 ÷ 2 = 522 757 + 0;
- 522 757 ÷ 2 = 261 378 + 1;
- 261 378 ÷ 2 = 130 689 + 0;
- 130 689 ÷ 2 = 65 344 + 1;
- 65 344 ÷ 2 = 32 672 + 0;
- 32 672 ÷ 2 = 16 336 + 0;
- 16 336 ÷ 2 = 8 168 + 0;
- 8 168 ÷ 2 = 4 084 + 0;
- 4 084 ÷ 2 = 2 042 + 0;
- 2 042 ÷ 2 = 1 021 + 0;
- 1 021 ÷ 2 = 510 + 1;
- 510 ÷ 2 = 255 + 0;
- 255 ÷ 2 = 127 + 1;
- 127 ÷ 2 = 63 + 1;
- 63 ÷ 2 = 31 + 1;
- 31 ÷ 2 = 15 + 1;
- 15 ÷ 2 = 7 + 1;
- 7 ÷ 2 = 3 + 1;
- 3 ÷ 2 = 1 + 1;
- 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.
33 456 452(10) = 1 1111 1110 1000 0001 0100 0100(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 25.
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, 25,
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.
33 456 452(10) = 0000 0001 1111 1110 1000 0001 0100 0100
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.
-33 456 452(10) = !(0000 0001 1111 1110 1000 0001 0100 0100)
Number -33 456 452(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:
-33 456 452(10) = 1111 1110 0000 0001 0111 1110 1011 1011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.