Base ten decimal system signed integer number 9 999 converted to signed binary = 0010 0111 0000 1111 How to convert the signed integer in decimal system (in base 10): 9 999(10) to a signed binary 1. Divide the number repeatedly by 2, keeping track of each remainder, until we get a quotient that is equal to zero: division = quotient + remainder; 9 999 ÷ 2 = 4 999 + 1; 4 999 ÷ 2 = 2 499 + 1; 2 499 ÷ 2 = 1 249 + 1; 1 249 ÷ 2 = 624 + 1; 624 ÷ 2 = 312 + 0; 312 ÷ 2 = 156 + 0; 156 ÷ 2 = 78 + 0; 78 ÷ 2 = 39 + 0; 39 ÷ 2 = 19 + 1; 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, by taking all the remainders starting from the bottom of the list constructed above: 9 999(10) = 10 0111 0000 1111(2) 3. Determine the signed binary number bit length: The base 2 number's actual length, in bits: 14. 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; ... First bit (the leftmost) is reserved for the sign: 0 = positive integer number, 1 = negative integer number The least number that is a power of 2 and is larger than the actual length so that the first bit (leftmost) could be zero is: 16. 4. 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: 9 999(10) = 0010 0111 0000 1111 Conclusion: Number 9 999, a signed integer, converted from decimal system (base 10) to signed binary: 9 999(10) = 0010 0111 0000 1111 First bit (the leftmost) is reserved for the sign: 0 = positive integer number, 1 = negative integer number Spaces used to group numbers digits: for binary, by 4; for decimal, by 3.