1. Start with the positive version of the number:
|-99 999 934| = 99 999 934
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;
- 99 999 934 ÷ 2 = 49 999 967 + 0;
- 49 999 967 ÷ 2 = 24 999 983 + 1;
- 24 999 983 ÷ 2 = 12 499 991 + 1;
- 12 499 991 ÷ 2 = 6 249 995 + 1;
- 6 249 995 ÷ 2 = 3 124 997 + 1;
- 3 124 997 ÷ 2 = 1 562 498 + 1;
- 1 562 498 ÷ 2 = 781 249 + 0;
- 781 249 ÷ 2 = 390 624 + 1;
- 390 624 ÷ 2 = 195 312 + 0;
- 195 312 ÷ 2 = 97 656 + 0;
- 97 656 ÷ 2 = 48 828 + 0;
- 48 828 ÷ 2 = 24 414 + 0;
- 24 414 ÷ 2 = 12 207 + 0;
- 12 207 ÷ 2 = 6 103 + 1;
- 6 103 ÷ 2 = 3 051 + 1;
- 3 051 ÷ 2 = 1 525 + 1;
- 1 525 ÷ 2 = 762 + 1;
- 762 ÷ 2 = 381 + 0;
- 381 ÷ 2 = 190 + 1;
- 190 ÷ 2 = 95 + 0;
- 95 ÷ 2 = 47 + 1;
- 47 ÷ 2 = 23 + 1;
- 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.
99 999 934(10) = 101 1111 0101 1110 0000 1011 1110(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 27.
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, 27,
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.
99 999 934(10) = 0000 0101 1111 0101 1110 0000 1011 1110
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.
-99 999 934(10) = !(0000 0101 1111 0101 1110 0000 1011 1110)
Number -99 999 934(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:
-99 999 934(10) = 1111 1010 0000 1010 0001 1111 0100 0001
Spaces were used to group digits: for binary, by 4, for decimal, by 3.