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;
- 17 220 ÷ 2 = 8 610 + 0;
- 8 610 ÷ 2 = 4 305 + 0;
- 4 305 ÷ 2 = 2 152 + 1;
- 2 152 ÷ 2 = 1 076 + 0;
- 1 076 ÷ 2 = 538 + 0;
- 538 ÷ 2 = 269 + 0;
- 269 ÷ 2 = 134 + 1;
- 134 ÷ 2 = 67 + 0;
- 67 ÷ 2 = 33 + 1;
- 33 ÷ 2 = 16 + 1;
- 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.
17 220(10) = 100 0011 0100 0100(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 17 220(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in two's complement representation:
17 220(10) = 0100 0011 0100 0100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.