Exam (elaborations) PHYSICAL SCIENCES PAPER 2 (CHEMISTRY) GRADE 12

1. Data Representation 1.1. Number Systems Binary System Base 2 number system Has two possible values only (0 and 1) 0 represents OFF and 1 represents ON A point to be noted is that the most left bit is called the MSB (Most Significant Bit) Denary System Base 10 number system Has values from 0 to 9 Hexadecimal (aka Hex) Base 16 number system Has values from 0 to 9 followed by A to F A represents 10, B represents 11 and so on until 15 which is F Binary Value Hexadecimal Value Denary Value 0000 0 0 0001 1 1 0010 2 2 0011 3 3 0100 4 4 0101 5 5 0110 6 6 0111 7 7 1000 8 8 1001 9 9 1010 A 10 1011 B 11 1100 C 12 1101 D 13 1110 E 14 1111 F 15 Number Conversions 1.2. Converting Binary to Denary Take the binary value and place it in columns of 2 raised to the power of the number of values from the right starting from 0.e.g. For binary value , place it in a table like this: 4 2 1 1 1 1 0 1 1 1 0 As it can be seen that it starts from 1 and then goes till 128 from left to right Now values with 1 are to be added together giving the final answer, as for the example, it is 128 + 64 + 32 + 8 + 4 + 2 = 238 Converting Denary to Binary Take the value and successively divide it by 2 creating a table like follows: 2 142 2 71 Remainder: 0 2 35 Remainder: 1 2 17 Remainder: 1 2 8 Remainder: 1 2 4 Remainder: 0 2 2 Remainder: 0 2 1 Remainder: 0 0 Remainder: 1 Note that when the value itself is not divisible by 2, it is divided by the previous value of the current number and 1 is added to the remainder column for that specific number When you reach 0, the remainder has to be read from bottom to top giving us the binary value ( as in this case, it is 1 0 0 0 1 1 1 0 ) Converting Hexadecimal to Binary Separate each value from each other and convert them to denary Each separate denary value to be converted to binary All the binary values to be merged together e.g. Hexadecimal : 2 1 F D Denary : 2 1 15 13 Binary : Final Answer: Converting Binary To Hexadecimal Divide the binary value into groups of 4 starting from the right. If at the end, the last division is less than 4, add 0s until it reaches 4 For each group, find the denary value as shown above, and then convert each denary value to its corresponding hexadecimal value (if less than 10, then itself, else, 10 is A, 11 is B, 12 is C, 13 is D, 14 is E and 15 is F