For longer binary numbers, it is usually helpful to first convert to hex and then use the power-of-16 placeholders to make the conversion. For example, 11 1010 0110 = 3A6_{H}.
One way to convert decimal to binary is to perform successive divisions by 2, checking for an odd or even number at each step. If odd, then record a 1 for the bit, and subtract one from the quotient. If even, then record a 0 for the bit. Continue dividing by 2 until the number become fractional.
For example:
2001 | odd | 1 | least significant digit | |
sub 1, div 2 | 1000 | even | 0 | |
div 2 | 500 | even | 0 | |
div 2 | 250 | even | 0 | |
div 2 | 125 | odd | 1 | |
sub 1, div 2 | 62 | even | 0 | |
div 2 | 31 | odd | 1 | |
sub 1, div 2 | 15 | odd | 1 | |
sub 1, div 2 | 7 | odd | 1 | |
sub 1, div 2 | 3 | odd | 1 | |
sub 1, div 2 | 1 | odd | 1 | most significant digit |
Answer: 0111 1101 0001
Alternatively, convert 2000_{10} first to hex, then that number (7D1_{H}) to binary.
In binary, 1 + 1 + 1 = 11
That is, 1 carry 1.
For binary to hex conversion, go from right to left setting up groups of 4 bits, then associate the appropriate hex digit with each nibble.
0 | 1100 | binary representation of 12_{10} | |
1 | 0011 | one's complement | |
+ | 1 | add one to find the | |
1 | 0100 | two's complement |
The two's complement of 0 1111 (15) is 1 0001.
The two's complement of 1 0011 (3) is 1 1101.