1. 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;
- 16 721 ÷ 2 = 8 360 + 1;
- 8 360 ÷ 2 = 4 180 + 0;
- 4 180 ÷ 2 = 2 090 + 0;
- 2 090 ÷ 2 = 1 045 + 0;
- 1 045 ÷ 2 = 522 + 1;
- 522 ÷ 2 = 261 + 0;
- 261 ÷ 2 = 130 + 1;
- 130 ÷ 2 = 65 + 0;
- 65 ÷ 2 = 32 + 1;
- 32 ÷ 2 = 16 + 0;
- 16 ÷ 2 = 8 + 0;
- 8 ÷ 2 = 4 + 0;
- 4 ÷ 2 = 2 + 0;
- 2 ÷ 2 = 1 + 0;
- 1 ÷ 2 = 0 + 1;
2. Construct the base 2 representation of the positive number:
Take all the remainders starting from the bottom of the list constructed above.
16 721(10) = 100 0001 0101 0001(2)
3. 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) 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, 15,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 16.
4. 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.
Number 16 721(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:
Spaces were used to group digits: for binary, by 4, for decimal, by 3.