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;
- 34 174 ÷ 2 = 17 087 + 0;
- 17 087 ÷ 2 = 8 543 + 1;
- 8 543 ÷ 2 = 4 271 + 1;
- 4 271 ÷ 2 = 2 135 + 1;
- 2 135 ÷ 2 = 1 067 + 1;
- 1 067 ÷ 2 = 533 + 1;
- 533 ÷ 2 = 266 + 1;
- 266 ÷ 2 = 133 + 0;
- 133 ÷ 2 = 66 + 1;
- 66 ÷ 2 = 33 + 0;
- 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.
34 174(10) = 1000 0101 0111 1110(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 34 174(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:
34 174(10) = 0000 0000 0000 0000 1000 0101 0111 1110
Spaces were used to group digits: for binary, by 4, for decimal, by 3.