combinatorial

# combinatorial - 5 Combinatorial Components Use for data...

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5 Combinatorial Components Use for data transformation, manipulation, interconnection, and for control: arithmetic operations - addition, subtraction, multiplication and division. logic operations - AND, OR, XOR, and NOT. comparison operations - greater than, equal to, and less than. bit manipulation operations - shift, rotation, extraction, and insertion. interconnect components - selectors, and buses - used to connect different components together. conversion components - decoders and encoders - used for conversion between different codes. universal components - ROMs and programmable-logic arrays (PLAs) - used primarily in the design of control units. 5.0 Full adder i = x i ' y i ' c i + x i ' y i c i ' + x i y i ' c i ' + x i y i c i = ( x i ' y i + x i y i ') c i ' + ( x i ' y i ' + x i y i ) c i = ( x i y i ) c i ' + ( x i ~ y i ) c i = ( x i y i ) c i c i +1 = x i ' y i c i + x i y i ' c i + x i y i c i ' + x i y i c i = x i y i ( c i ' + c i ) + c i ( x i ' y i + x i y i ') = x i y i 1 + c i ( x i y i ) s i c i c i +1 x i y i Circuit for Full Adder Full subtractor b in xyb out d Comment 00 0 0 0 x - b in - y = d = 0-0 = 0 0 0 1 1 1 0-0-1 = borrow 2-1 = 1 0 1 0 0 1 1-0-0=1 with no borrow 0 1 1 0 0 1-0-1=0 with no borrow 10 0 1 1 x =0-1=-1 because of b in =1, therefore, borrow 2-1=1. Finally, 1-0=1 1 1 0 x - b in - y =borrow 2-1-1=0 1 1 0 0 0 1-1-0=0 with no borrow 11 1 1 1 x - b in =1-1=0. Then 0-1=borrow 2-1=1 FA XY Cin Cout S x i y i c i c i +1 s i 00000 00101 01001 01110 10001 10110 11010 11111

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01 1 1 1 00 0 1 b in 45 10 11 1 32 76 xy x'y yb x'b 1 1 0 1 b 1 1 in in out yb y x b x b + + = y x b y x b y x b y x y x b xy y x b b y x b y x xyb b y x d in in in in in in in in in = + = + + + = + + + = ) ( ) ( ) ( ) ( b b out d Circuit for Full Subtractor 5.1 Ripple-carry adders FA x 0 y 0 s 0 x 1 y 1 s 1 x 2 y 2 s 2 x 3 y 3 s 3 x 4 y 4 s 4 x 5 y 5 s 5 x 6 y 6 s 6 x 7 y 7 s 7 c c c 2 c 3 c 4 c 5 c 6 c 7 c 1 5.3 Adder / Subtractor x 0 y 0 f 0 x 1 y 1 f 1 x 2 y 2 f 2 x 3 y 3 f 3 x 4 y 4 f 4 x 5 y 5 f 5 x 6 y 6 f 6 x 7 y 7 f 7 c c 2 c 3 c 4 c 5 c 6 c 7 c 1 c 0 S 5.4 Logic Unit
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## This note was uploaded on 09/10/2008 for the course CSIS 2810 taught by Professor Balasa during the Spring '08 term at Southern Utah.

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combinatorial - 5 Combinatorial Components Use for data...

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