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Unformatted text preview: 6 1 3 10 10 10 2 1 6 x 100+ 1 x 10 + 3 x 1 =613 Base 10 digits {0...9} 1 1 0 1 2 2 2 1 2 2 3 1 x 8+ 1 x 4+ 0 x 2+ 1 x 1 = 13 Base 2 digits {0, 1} decimal binary 1 1 2 10 3 11 4 100 5 101 6 110 7 111 8 1000 9 1001 10 1010 11 1011 12 1100 13 1101 14 1110 15 1111 The binary equivalents of some decimal numbers. parent Left child right child A binary tree consists of a set of nodes each of which can have at most two children. root leaf leaf leaf The top node of the tree is called the root. A leaf is a node with no descendants. 1 1 0 1 2 2 2 1 2 2 3 The binary digits ( bits ) in the computers memory are initially set to zero. To represent a number, the appropriate bits are set to 1. 13 (dec) 4 (dec) = Multiplying by 2 in machine language is accomplished by shifting left one bit. 000100 4 (dec) = 8 (dec) = Multiplying by 2 in machine language is accomplished by shifting left one bit. 000100 001000 4 (dec) = 8 (dec) = 16 (dec) = Multiplying by 2 in machine language is accomplished by shifting left one bit. 000100 001000 010000 4 (dec) = 8 (dec) = 16 (dec) = 000100 001000 010000 5 (dec) = 9 (dec) = 17 (dec) = 000101 001001 010001 We obtain the next integer by adding a 1 to the binary number. n 2n 2n+1 Construct a tree using the following: If the parent s node number is n, the left childs is 2*n and the right childs is 2*n + 1. 1 We assign 1 to the roots node number 1 2 Then, the left childs node number is 2 1 2 3 And the right childs node number is 3. 1 2 3 4 5 6 7 A graphical way of getting the binary equivalents of decimal numbers. Place a 0 on each left edge. 1 2 3 4 5 6 7 A graphical way of getting the binary equivalents of decimal numbers. Place a 0 on each left edge. 1 2 3 4 5 6 7 A graphical way of getting the binary equivalents of decimal numbers. Place a 0 on each left edge. 1 2 3 4 5 6 7 1 A graphical way of getting the binary equivalents of decimal numbers. Place a 0 on each left edge and a 1 on each right edge of a binary tree. 1...
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 Spring '11
 SanaOdeh

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