Page 1 1 A Simple ALU Binary Logic Page 2 1 A Simple ALU Binary Logic 2 Outline l Binary Logic l Representation of Logic Gates l Constructing a 1-bit adder l Constructing an n-bit adder Page 3 1 A Simple ALU Binary Logic 2 Outline l Binary Logic l Representation of Logic Gates l Constructing a 1-bit adder l Constructing an n-bit adder 3 Binary Logic l A computer works using digital electronics. l There are only High and Low voltages l All computer logic is based on the manipulation of these l Abstractly, » High is interpreted as 1 (true) » Low is interpreted as 0 (false) Page 4 1 A Simple ALU Binary Logic 2 Outline l Binary Logic l Representation of Logic Gates l Constructing a 1-bit adder l Constructing an n-bit adder 3 Binary Logic l A computer works using digital electronics. l There are only High and Low voltages l All computer logic is based on the manipulation of these l Abstractly, » High is interpreted as 1 (true) » Low is interpreted as 0 (false) 4 Logic Circuit l A logic circuit takes in a number of input lines (A, B, C, ...) » and has a number of output lines (X,Y,Z,...) A B C X Y Z Page 5 1 A Simple ALU Binary Logic 2 Outline l Binary Logic l Representation of Logic Gates l Constructing a 1-bit adder l Constructing an n-bit adder 3 Binary Logic l A computer works using digital electronics. l There are only High and Low voltages l All computer logic is based on the manipulation of these l Abstractly, » High is interpreted as 1 (true) » Low is interpreted as 0 (false) 4 Logic Circuit l A logic circuit takes in a number of input lines (A, B, C, ...) » and has a number of output lines (X,Y,Z,...) A B C X Y Z 5 Logic Basics l Every expression evaluates to 1 or 0 l NOT » ~A (“A bar”) – is the complement of A, i.e. 1-A l OR » A + B – is 1 if and only if at least one of A or B is 1, else 0 l AND » A.B – is 1 if and only if both A and B are 1, else 0Read More

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