Circuits and gate or gate not gate Combining Determining I O Relationship P Q R P Q R 1 Draw the Circuit for P 1 1 1 Simplify 1 0 before 0 building the circuit 0 0 P Q R are inputs Q 1 1 0 0 1 1 0 0 R 1 0 1 0 1 0 1 0 Output 1 1 0 1 0 0 0 0 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 2 Addition of Binary Numbers Carry if the number would be too large for the number system if it is greater than 1 1001 1001 1011 1101 10 11 11 111 Addition of Oct and Hex Numbers Carry if the number would be too large for the number system larger than 7 or 15 7238 2658 ABC16 CDE16 128 338 1216 ED16 3 Using a Circuit for Addition Write as a Logic Expression Translate to Circuits input output P Q Carry Sum 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 Half Adder P Q sum carry P and Q are binary values 1 bit each sum P v Q P Q carry P Q 4 Full Adder P Q C1 half adder 1 C S1 C2 half adder 2 R S P Q and R are binary digits P Q R gives sum value and carry value Parallel Adders Chain these half adders and full adders together for multi bit addition X1X2X3 Y1Y2Y3 CA1A2A3 X3 Y3 X2 Y2 X1 Y1 half adder A3 carry A2 full adder carry full adder A1 carry 5 2 s Compliment To Represent Negative Values using Binary 1 Find the binary equivalent of the absolute value 2 Pad on the left to completely fill the bits 3 Switch all of the 1 s to 0 s and 0 s to 1 s 4 Add 1 to the result i e Find the 8 bit 2 s compliment representation of 43 1 4310 1010112 2 001010112 3 110101002 4 110101012 4310 6
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