Number Systems Base 2, 10, 16

Base 10 Decimal System has 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 1,000,000 100,000 10,000 1000 100 10 1 106 105 104 103 102 101

Base 2 The Binary system has only 2 digits: 0 and 1 32 16 8 4 1 26 25 64 32   16  8 4  2  1 26 25 24 23 22 21 20  

Adding in Binary Adding in Binary is just like adding in decimal 1 16 +14 30 1 101 + 1 110

Subtracting in Binary 1 20 - 14 6 01 100 - 1 11 Subtracting in Binary is just like subtracting in decimal 1 20 - 14 6 01 100 - 1 11 1 1 1

Multiplying in Binary 26 x 14 104 260 364 1101 x 11 11010 100111 Multiplying in Binary is just like multiplying in decimal 26 x 14 104 260 364 1101 x 11 11010 100111

Base 16 The Hexadecimal system has 16 digits: 0-9, plus A, B, C, D, E, F 65,536 4096 256 16 1 164 163 162 161 160  

Converting between Base 2 and 16 Each hexadecimal digit converts directly to a four-digit binary number. Base 16 Base 10 Base 2 0000 8 1000 1 0001 9 1001 2 0010 A 10 1010 3 0011 B 11 1011 4 0100 C 12 1100 5 0101 D 13 1101 6 0110 E 14 1110 7 0111 F 15 1111

Converting between Base 2 and 16 Similarly, every four binary digits can be converted to one hexadecimal digit. 10001100 110101001 8 C 1 A 9