Express the number 208 as a) an 8-bit binary number b) an octal string c) a hexadecimal string

Number conversions are a staple of both A-Level and GCSE computing papers. a) Expressing as a binary number is the hardest part of a conversion. Octal and hexadecimal can all come after easily. To express as a binary number, the easiest way is to use the "take away" method from the left hand side. Digit 1 - 128: is (208 - 128) >= 0? Yes - 1 carry 80 Digit 2 - 64: is (80 - 64) >= 0? Yes - 1 carry 16 Digit 3 - 32: is (16 - 32) >= 0? No - 0 carry 16 Digit 4 - 16: is (16 - 16) >= 0? Yes - 1 carry 0 Since we have reached carry 0, we can assume all other digits are 0 giving us 1101 0000_2. b) Converting to octal is simple from binary: you take each 3 binary bits and turn them in to octal. Pad 1101 0000 to 9 bits: 011 010 000 Gives us 320₈ c) Exactly the same as b) but using 4 bits. Gives us D0₁₆