Base ten decimal system signed integer number 1 026 converted to signed binary in one's complement representation = 0000 0100 0000 0010 How to convert a signed integer in decimal system (in base 10): 1 026(10) to a signed binary one's complement representation 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; 1 026 ÷ 2 = 513 + 0; 513 ÷ 2 = 256 + 1; 256 ÷ 2 = 128 + 0; 128 ÷ 2 = 64 + 0; 64 ÷ 2 = 32 + 0; 32 ÷ 2 = 16 + 0; 16 ÷ 2 = 8 + 0; 8 ÷ 2 = 4 + 0; 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: 1 026(10) = 100 0000 0010(2) 3. Determine the signed binary number bit length: The base 2 number's actual length, in bits: 11. 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. 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: 1 026(10) = 0000 0100 0000 0010 Conclusion: Number 1 026, a signed integer, converted from decimal system (base 10) to a signed binary one's complement representation: 1 026(10) = 0000 0100 0000 0010 Spaces used to group numbers digits: for binary, by 4; for decimal, by 3.