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;
- 7 734 520 ÷ 2 = 3 867 260 + 0;
- 3 867 260 ÷ 2 = 1 933 630 + 0;
- 1 933 630 ÷ 2 = 966 815 + 0;
- 966 815 ÷ 2 = 483 407 + 1;
- 483 407 ÷ 2 = 241 703 + 1;
- 241 703 ÷ 2 = 120 851 + 1;
- 120 851 ÷ 2 = 60 425 + 1;
- 60 425 ÷ 2 = 30 212 + 1;
- 30 212 ÷ 2 = 15 106 + 0;
- 15 106 ÷ 2 = 7 553 + 0;
- 7 553 ÷ 2 = 3 776 + 1;
- 3 776 ÷ 2 = 1 888 + 0;
- 1 888 ÷ 2 = 944 + 0;
- 944 ÷ 2 = 472 + 0;
- 472 ÷ 2 = 236 + 0;
- 236 ÷ 2 = 118 + 0;
- 118 ÷ 2 = 59 + 0;
- 59 ÷ 2 = 29 + 1;
- 29 ÷ 2 = 14 + 1;
- 14 ÷ 2 = 7 + 0;
- 7 ÷ 2 = 3 + 1;
- 3 ÷ 2 = 1 + 1;
- 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.
7 734 520(10) = 111 0110 0000 0100 1111 1000(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 23.
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, 23,
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 7 734 520(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:
7 734 520(10) = 0000 0000 0111 0110 0000 0100 1111 1000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.