1. DECIMAL BASE Based on power of 10 In the number 2,468 – from right to left -- the 8 represents the ones, the 6 represents the tens, the 4 represents the hundreds, the 2 represent the thousands. 2, 468 = 8*1 + 6*10 + 4*100 + 2*1000 You can use ANY number for a base

2. Hexadecimal Numbers – Base 16 Decimal NumberHexadecimal Number 00 11 22 33 44 55 66 77 88 99 10A or a 11B or b 12C or c 13D or d 14E or e 15F or f

3. Hexadecimal Numbers cont. 0x283 – C++ uses 0X or 0x to indicate that the number is hexadecimal. ( i. e. if you have the number 283 how would you know if it is a hexadecimal or decimal ? )

4. Hexadecimal to decimal conversion 0X283 = 3 * 16^0 + 8*16^1 + 2*16^2 = = 3*1 + 8*16 + 2*256 = 637 283h = 637d ( another way to differentiate between hexadecimal and decimal but this notation is good in assembly language and for humans too )

5. Binary Numbers ( base 2 ) The computer’s number system Whether you write a n umber in decimal, hexadecimal, octal, or even other base, the computer stores it in binary. 10011011 The memory is commonly organized in units called bytes ( 1 byte = 8 bits )

6. Conversion Binary numbers to Decimal 100110111 = 1*2^0 + 1 * 2^1 + 1 * 2^2 + 0*2^3 + 1*2^4 + 1*2^5 + 0*2^6 + 0*2^7 + 1*2^8 = 1*1 + 1 * 2 + 1 * 4 + 0 * 8 + 1 * 16 + 1* 32 + 0 * 64 + 0 *128 + 1 * 256 = 1 + 2 + 4 + 0 + 16 + 32 + 0 + 0 + 256 = 311

7. Easier Way to convert binary to base 10 2561286432168421 100110111

8. Base Table Decimal DigitBinary DigitHexadecimal Digit 000000 100011 200102 300113 401004 501015 601106 701117 810008 910019 101010A 111011B 121100C 131101D 141110E 151111F

9. Conversion from Decimal to Binary and Hexadecimal LONG DIVISION….. Pay attention in class Or Google – there are excellent sites that you can learn how to do it: Here is one of them: http://www.cs.iupui.edu/~n241/readings/binc onv.html#Dec2Bin1 http://www.cs.iupui.edu/~n241/readings/binc onv.html#Dec2Bin1