Base ten decimal system signed integer number -500 converted to signed binary in two's complement representation = 1111 1110 0000 1100 How to convert a signed integer in decimal system (in base 10): -500(10) to a signed binary two's complement representation 1. We start with the positive version of the number: |-500| = 500 2. Divide the number repeatedly by 2, keeping track of each remainder, until we get a quotient that is equal to zero: division = quotient + remainder; 500 ÷ 2 = 250 + 0; 250 ÷ 2 = 125 + 0; 125 ÷ 2 = 62 + 1; 62 ÷ 2 = 31 + 0; 31 ÷ 2 = 15 + 1; 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, by taking all the remainders starting from the bottom of the list constructed above: 500(10) = 1 1111 0100(2) 4. Determine the signed binary number bit length: The base 2 number's actual length, in bits: 9. 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) indicates the sign, 1 = negative, 0 = positive. 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. 5. 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: 500(10) = 0000 0001 1111 0100 6. To get the negative integer number representation on 16 bits (2 Bytes), signed binary one's complement, replace all the bits on 0 with 1s and all the bits set on 1 with 0s (reversing the digits): !(0000 0001 1111 0100) = 1111 1110 0000 1011 7. To get the negative integer number representation on 16 bits (2 Bytes), signed binary two's complement, add 1 to the number calculated above: 1111 1110 0000 1011 + 1 = 1111 1110 0000 1100 Conclusion: Number -500, a signed integer, converted from decimal system (base 10) to a signed binary two's complement representation: -500(10) = 1111 1110 0000 1100 Spaces used to group numbers digits: for binary, by 4.