CMSC 250 Discrete Structures Logic Applications Circuits Adders Circuits AND OR gate NOT 11 June 2007 gate gate Logic Applications 2 Combining Determining I O Relationship P Q R 11 June 2007 Logic Applications 3 Draw the Circuit for P Q R are inputs Simplify before building the circuit 11 June 2007 P 1 1 1 1 0 0 0 0 Q 1 1 0 0 1 1 0 0 Logic Applications R 1 0 1 0 1 0 1 0 Output 1 1 0 1 0 0 0 0 4 Number Conversions Base of the Number System 10 decimal 2 binary 8 octal 16 hexadecimal Tells how many different numerals are used Determines the value of each place Conversions from anything to Base 10 Use the definition of the number system Conversions from Base 10 to anything Use repeated integer division 11 June 2007 Logic Applications 5 Addition of Binary Numbers Carry if the number would be too large for the number system if it is greater than 1 1001 10 11 June 2007 1001 11 Logic Applications 1011 11 1011 111 6 Addition of Binary Numbers Carry if the number would be too large for the number system larger than 7 or 15 7238 128 11 June 2007 2658 338 ABC16 1216 Logic Applications CDE16 ED16 7 Using a Circuit for Addition Write as a logic expression Translate to circuits Input 11 June 2007 Output P Q Carry Sum 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 Logic Applications 8 Half Adder P Q sum carry P and Q are binary values 1 bit each sum P v Q P Q carry P Q 11 June 2007 Logic Applications 9 Full Adder P Q R half adder 1 C1 C S1 C2 half adder 2 S P Q and R are binary digits P Q R gives sum value and carry value 11 June 2007 Logic Applications 10 Parallel Adders Chain these half adders and full adders together for multi bit addition X1X2X3 Y1Y2Y3 CA1A2A3 X3 Y3 X2 Y2 half adder A3 carry A2 full adder carry X1 Y1 full adder A1 carry 11 June 2007 Logic Applications 11 2 s Compliment To represent negative values using binary 1 2 3 4 Find the binary equivalent of the absolute value Pad on the left to completely fill the bits Switch all of the 1 s to 0 s and 0 s to 1 s Add 1 to the result Find the 8 bit 2 s compliment representation of 43 1 4310 2 1010112 3 001010112 4 110101002 5 110101012 4310 11 June 2007 Logic Applications 12
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