Base ten decimal system signed integer number 5 535 756 401 converted to signed binary = 0000 0000 0000 0000 0000 0000 0000 0001 0100 1001 1111 0100 1111 0000 0111 0001 How to convert the signed integer in decimal system (in base 10): 5 535 756 401(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; 5 535 756 401 ÷ 2 = 2 767 878 200 + 1; 2 767 878 200 ÷ 2 = 1 383 939 100 + 0; 1 383 939 100 ÷ 2 = 691 969 550 + 0; 691 969 550 ÷ 2 = 345 984 775 + 0; 345 984 775 ÷ 2 = 172 992 387 + 1; 172 992 387 ÷ 2 = 86 496 193 + 1; 86 496 193 ÷ 2 = 43 248 096 + 1; 43 248 096 ÷ 2 = 21 624 048 + 0; 21 624 048 ÷ 2 = 10 812 024 + 0; 10 812 024 ÷ 2 = 5 406 012 + 0; 5 406 012 ÷ 2 = 2 703 006 + 0; 2 703 006 ÷ 2 = 1 351 503 + 0; 1 351 503 ÷ 2 = 675 751 + 1; 675 751 ÷ 2 = 337 875 + 1; 337 875 ÷ 2 = 168 937 + 1; 168 937 ÷ 2 = 84 468 + 1; 84 468 ÷ 2 = 42 234 + 0; 42 234 ÷ 2 = 21 117 + 0; 21 117 ÷ 2 = 10 558 + 1; 10 558 ÷ 2 = 5 279 + 0; 5 279 ÷ 2 = 2 639 + 1; 2 639 ÷ 2 = 1 319 + 1; 1 319 ÷ 2 = 659 + 1; 659 ÷ 2 = 329 + 1; 329 ÷ 2 = 164 + 1; 164 ÷ 2 = 82 + 0; 82 ÷ 2 = 41 + 0; 41 ÷ 2 = 20 + 1; 20 ÷ 2 = 10 + 0; 10 ÷ 2 = 5 + 0; 5 ÷ 2 = 2 + 1; 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: 5 535 756 401(10) = 1 0100 1001 1111 0100 1111 0000 0111 0001(2) 3. Determine the signed binary number bit length: The base 2 number's actual length, in bits: 33. 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: 64. 4. Positive binary computer representation on 64 bits (8 Bytes) - if needed, add extra 0s in front (to the left) of the base 2 number, up to the required length: 5 535 756 401(10) = 0000 0000 0000 0000 0000 0000 0000 0001 0100 1001 1111 0100 1111 0000 0111 0001 Conclusion: Number 5 535 756 401, a signed integer, converted from decimal system (base 10) to signed binary: 5 535 756 401(10) = 0000 0000 0000 0000 0000 0000 0000 0001 0100 1001 1111 0100 1111 0000 0111 0001 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.
The base 2 number's actual length, in bits: 33.
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: 64.