1. Start with the positive version of the number:
|-29 526| = 29 526
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;
- 29 526 ÷ 2 = 14 763 + 0;
- 14 763 ÷ 2 = 7 381 + 1;
- 7 381 ÷ 2 = 3 690 + 1;
- 3 690 ÷ 2 = 1 845 + 0;
- 1 845 ÷ 2 = 922 + 1;
- 922 ÷ 2 = 461 + 0;
- 461 ÷ 2 = 230 + 1;
- 230 ÷ 2 = 115 + 0;
- 115 ÷ 2 = 57 + 1;
- 57 ÷ 2 = 28 + 1;
- 28 ÷ 2 = 14 + 0;
- 14 ÷ 2 = 7 + 0;
- 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.
29 526(10) = 111 0011 0101 0110(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 15.
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) is reserved for 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, 15,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 16.
5. Get the positive binary computer representation on 16 bits (2 Bytes):
If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 16:
29 526(10) = 0111 0011 0101 0110
6. Get the negative integer number representation:
To get the negative integer number representation on 16 bits (2 Bytes),
... change the first bit (the leftmost), from 0 to 1...
Number -29 526(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-29 526(10) = 1111 0011 0101 0110
Spaces were used to group digits: for binary, by 4, for decimal, by 3.