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;
- 7 777 ÷ 2 = 3 888 + 1;
- 3 888 ÷ 2 = 1 944 + 0;
- 1 944 ÷ 2 = 972 + 0;
- 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;
2. Construct the base 2 representation of the positive number:
Take all the remainders starting from the bottom of the list constructed above.
7 777(10) = 1 1110 0110 0001(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 13.
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, 13,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 16.
4. Get the positive binary computer representation on 16 bits (2 Bytes):
If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 16.
Number 7 777(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:
7 777(10) = 0001 1110 0110 0001
Spaces were used to group digits: for binary, by 4, for decimal, by 3.