1. Start with the positive version of the number:
|-72 597| = 72 597
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;
- 72 597 ÷ 2 = 36 298 + 1;
- 36 298 ÷ 2 = 18 149 + 0;
- 18 149 ÷ 2 = 9 074 + 1;
- 9 074 ÷ 2 = 4 537 + 0;
- 4 537 ÷ 2 = 2 268 + 1;
- 2 268 ÷ 2 = 1 134 + 0;
- 1 134 ÷ 2 = 567 + 0;
- 567 ÷ 2 = 283 + 1;
- 283 ÷ 2 = 141 + 1;
- 141 ÷ 2 = 70 + 1;
- 70 ÷ 2 = 35 + 0;
- 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.
72 597(10) = 1 0001 1011 1001 0101(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.
72 597(10) = 0000 0000 0000 0001 0001 1011 1001 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.
-72 597(10) = !(0000 0000 0000 0001 0001 1011 1001 0101)
Number -72 597(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:
-72 597(10) = 1111 1111 1111 1110 1110 0100 0110 1010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.