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;
- 35 127 ÷ 2 = 17 563 + 1;
- 17 563 ÷ 2 = 8 781 + 1;
- 8 781 ÷ 2 = 4 390 + 1;
- 4 390 ÷ 2 = 2 195 + 0;
- 2 195 ÷ 2 = 1 097 + 1;
- 1 097 ÷ 2 = 548 + 1;
- 548 ÷ 2 = 274 + 0;
- 274 ÷ 2 = 137 + 0;
- 137 ÷ 2 = 68 + 1;
- 68 ÷ 2 = 34 + 0;
- 34 ÷ 2 = 17 + 0;
- 17 ÷ 2 = 8 + 1;
- 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.
35 127(10) = 1000 1001 0011 0111(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 16.
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, 16,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 32.
4. 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.
Number 35 127(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:
35 127(10) = 0000 0000 0000 0000 1000 1001 0011 0111
Spaces were used to group digits: for binary, by 4, for decimal, by 3.