2. 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;
- 15 934 240 ÷ 2 = 7 967 120 + 0;
- 7 967 120 ÷ 2 = 3 983 560 + 0;
- 3 983 560 ÷ 2 = 1 991 780 + 0;
- 1 991 780 ÷ 2 = 995 890 + 0;
- 995 890 ÷ 2 = 497 945 + 0;
- 497 945 ÷ 2 = 248 972 + 1;
- 248 972 ÷ 2 = 124 486 + 0;
- 124 486 ÷ 2 = 62 243 + 0;
- 62 243 ÷ 2 = 31 121 + 1;
- 31 121 ÷ 2 = 15 560 + 1;
- 15 560 ÷ 2 = 7 780 + 0;
- 7 780 ÷ 2 = 3 890 + 0;
- 3 890 ÷ 2 = 1 945 + 0;
- 1 945 ÷ 2 = 972 + 1;
- 972 ÷ 2 = 486 + 0;
- 486 ÷ 2 = 243 + 0;
- 243 ÷ 2 = 121 + 1;
- 121 ÷ 2 = 60 + 1;
- 60 ÷ 2 = 30 + 0;
- 30 ÷ 2 = 15 + 0;
- 15 ÷ 2 = 7 + 1;
- 7 ÷ 2 = 3 + 1;
- 3 ÷ 2 = 1 + 1;
- 1 ÷ 2 = 0 + 1;
3. Construct the base 2 representation of the positive number:
Take all the remainders starting from the bottom of the list constructed above.
15 934 240(10) = 1111 0011 0010 0011 0010 0000(2)
4. 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) is reserved for 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.
5. 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:
15 934 240(10) = 0000 0000 1111 0011 0010 0011 0010 0000
6. Get the negative integer number representation:
To get the negative integer number representation on 32 bits (4 Bytes),
... change the first bit (the leftmost), from 0 to 1...
Number -15 934 240(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-15 934 240(10) = 1000 0000 1111 0011 0010 0011 0010 0000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.