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;
- 24 051 974 ÷ 2 = 12 025 987 + 0;
- 12 025 987 ÷ 2 = 6 012 993 + 1;
- 6 012 993 ÷ 2 = 3 006 496 + 1;
- 3 006 496 ÷ 2 = 1 503 248 + 0;
- 1 503 248 ÷ 2 = 751 624 + 0;
- 751 624 ÷ 2 = 375 812 + 0;
- 375 812 ÷ 2 = 187 906 + 0;
- 187 906 ÷ 2 = 93 953 + 0;
- 93 953 ÷ 2 = 46 976 + 1;
- 46 976 ÷ 2 = 23 488 + 0;
- 23 488 ÷ 2 = 11 744 + 0;
- 11 744 ÷ 2 = 5 872 + 0;
- 5 872 ÷ 2 = 2 936 + 0;
- 2 936 ÷ 2 = 1 468 + 0;
- 1 468 ÷ 2 = 734 + 0;
- 734 ÷ 2 = 367 + 0;
- 367 ÷ 2 = 183 + 1;
- 183 ÷ 2 = 91 + 1;
- 91 ÷ 2 = 45 + 1;
- 45 ÷ 2 = 22 + 1;
- 22 ÷ 2 = 11 + 0;
- 11 ÷ 2 = 5 + 1;
- 5 ÷ 2 = 2 + 1;
- 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.
24 051 974(10) = 1 0110 1111 0000 0001 0000 0110(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 25.
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, 25,
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 24 051 974(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:
24 051 974(10) = 0000 0001 0110 1111 0000 0001 0000 0110
Spaces were used to group digits: for binary, by 4, for decimal, by 3.