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Lecture 9 – Hex notation Hexadecimal notation is simply Base 16, you really need to understand several concepts before, discussing the Atmel assembler (next lecture). The assembler concept is based round binary (base 2) but often the information is presented in HEX (Base 16). This is to prevent users having to read long strings of 0’s and 1’s. You need to understand Base 2 representation (including 2’s complement) (last lecture) Base 16 representation Convert from o HEX to BINARY o BINARY to HEX BASE 16 representation Base 16 (HEX) is similar to BASE 2 (Binary) and Base 10 (decimal) Base 2 has 2 digits and uses the digits ( 0, 1) Base 10 has 10 digits and uses the digits ( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9) Base 16 has 16 digits and uses the digits ( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F) X2 The columns in Base 2 go x8 X2 x4 x The columns in Base 10 go x x2 x x X The columns in Base 16 go x x1 x x10 X x 53 X2 x1 X x x1 Idiots conversion table for Binary/HEX/Decimal Decimal 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Binary (*1) 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 HEX 0 1 2 3 4 5 6 7 8 9 A B C D E F (*1) We would not normally show leading zero’s but this will help with HEX/Binary Binary/HEX conversion later 54 X65,536 (i) (ii) (iii) (i) 2 X4,096 X256 F 1 0 X16 B 2 0 X1 7 E E REMEMBER that B = 11 (see table page 54) (11 x 16) + (7 x 1) = 183 Hence convert (ii) (iii) HEX Binary Conversion As 16 is a multiple of 2 e.g. 16 = 2 4 , there is an easy method to convert from HEX to Binary, each HEX digit can essentially be replaced with a group of 4 binary digits Binary (*1) 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 HEX 0 1 2 3 4 5 6 7 8 9 A B C D E F Convert 7F to binary From table 7 F 0111 1111 Hence 7F becomes 01111111 or Convert the following to binary 1111111 if we ignore leading zero’s 55 2B 1FD Converting Binary into HEX This is simply the reverse of HEX/Binary conversion. Still using the table we must divide the Binary number into groups of 4 digits and then convert these groups into HEX digits. There are, however, two simple rules Always start grouping from the least significant end of the string If you are left with a group of less than 4 digits add zeros to the most significant part of the group until it becomes a 4 digit number. Convert 1 1 0 0 1 1 1 1 0 1 into HEX Divide into groups of 4 11001101101 Padding out the last group with a zero we get 01 1 0 0 1 1 0 1 1 0 1 giving 6 6 D Hence convert the following strings 10011111 111110011 11111111111111111 HEX Addition 56 Start groups of 4 from here X256 + x16 x1 A 9 A 9 1 2 Basically the same as addition in decimal except that when the total comes to 16 or more ‘1’ is carried over to the next column Note the following 9 + 9 = 18, which is too big for HEX, we therefore carry 16 over to the next column (18 – 16 = 2) (which is placed in the X1 column) Notice when 16 is carried over it becomes ‘1’ in the x16 column Complete the addition remember A = 10 in decimal Convert to decimal to check your answer HEX subtraction Original sum was x16 A B X16 x1 1 0 - - 9 7 1 9 7 from 0 will not go therefore 16 is carried over from the x16 column notice the ‘B’ (11) becomes ‘A’ (10) notice also that the ‘10’ in the x1 column = 16 7 from 16 = 9 (written in the x1 column) Finally in the x16 column 9 from A (10) = 1 57 x1 B 0 9 7 Complete the following HEX sums X256 + x16 x1 2 C 3 F B 7 decimal check your answers by converting to decimal X256 - x16 x1 2 C 3 1 C 7 check your answers by converting to decimal 58 decimal