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;
- 10 000 160 ÷ 2 = 5 000 080 + 0;
- 5 000 080 ÷ 2 = 2 500 040 + 0;
- 2 500 040 ÷ 2 = 1 250 020 + 0;
- 1 250 020 ÷ 2 = 625 010 + 0;
- 625 010 ÷ 2 = 312 505 + 0;
- 312 505 ÷ 2 = 156 252 + 1;
- 156 252 ÷ 2 = 78 126 + 0;
- 78 126 ÷ 2 = 39 063 + 0;
- 39 063 ÷ 2 = 19 531 + 1;
- 19 531 ÷ 2 = 9 765 + 1;
- 9 765 ÷ 2 = 4 882 + 1;
- 4 882 ÷ 2 = 2 441 + 0;
- 2 441 ÷ 2 = 1 220 + 1;
- 1 220 ÷ 2 = 610 + 0;
- 610 ÷ 2 = 305 + 0;
- 305 ÷ 2 = 152 + 1;
- 152 ÷ 2 = 76 + 0;
- 76 ÷ 2 = 38 + 0;
- 38 ÷ 2 = 19 + 0;
- 19 ÷ 2 = 9 + 1;
- 9 ÷ 2 = 4 + 1;
- 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.
10 000 160(10) = 1001 1000 1001 0111 0010 0000(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 24.
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, 24,
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 10 000 160(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:
10 000 160(10) = 0000 0000 1001 1000 1001 0111 0010 0000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.