Computer Organization: Conversion of Base Notations, Truth Tables and Logic Circuits
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This article covers the conversion of base notations, truth tables and logic circuits in Computer Organization. It includes examples and references for better understanding.
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Question 1: Answer 1: 1)The answer are given below a)0*BED is the incorrect notation to convert it into base 3 notation. b)(321)7= (10100010)2 Digits321 Numbering210 First converting base 7 to base 10 3* 72+ 2 * 71+ 1 * 70 147 + 14 + 1 = 162 Now we will convert base 10 to base 2 with the division method DivisorDividendRemainder 2162 2810 2401 2200 2100 250 221 210 (321)7= (10100010)2 c)(1235)10= (2323)8 DivisorDividendRemainder 81235 81543 8192 823 (1235)10= (2323)8
a)(21.21)8= (17.265625)10 Place valueTensOneTenthHundredth Digit2121 Numbering81808-18-2 = 2 * 81 +1 * 80+ 2 * 8-1+ 2 * 8-2 = 16 + 1 + 0.125 + 0.03215 =17.265625 (21.21)8= (17.265625)10 2)One’ complement: The lowest value is 101 The highest value is 110 Two’s complement The lowest value is 011 The highest value is 101 Signed magnitude The lowest value is 001 The highest value is 111 Question 2: a)The result of the following truth table helps in predicting that the given two circuits are equivalent or not: Truth table for circuit one Operand AOperand BA*B (A AND B)NOT (A AND B) 0001 0101 1001 1110 Truth table for circuit two: Operand AOperand BOperand A NOTOperand B NOTA NOT OR B
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NOT 00111 01101 10011 11000 From the result of both the truth table we are able to measure that both the circuit are equivalent. b)The truth table for the given circuit is : ABNOT ANOT BNOT A AND NOT B A AND B(NOT A AND NOT B) OR (A AND B) 0011101 0110000 1011101 1100011 The result of the truth table is equivalent to the truth table of the OR gate. Therefore, the given complete circuit can be replaced with the OR gate. ABA OR B 000 011 101 111 The output of table 1 and 2 are equivalent as the signal will off only when both the input are off otherwise the result is true. The Logic Diagram of the resultant circuit is: c)X+Y+ X YZ=X+Y+Z For LHSX+Y+ X YZ XYZXYZX+YX YZX+Y+ Operand A Operand B Operand A OR Operand B
X YZ 000111101 001110101 010101101 011100101 100011101 101010101 110001011 111000000 For RHSX+Y+Z XYZXYZX+Y+Z 0001111 0011101 0101011 0111001 1000111 1010101 1100011 1110000 The equation is verified since the result of both the truth tables is equivalent. References Mano, M. (2012).Computer Architecture. Hand Book 3rded. Mendelson, E. (2016).Boolean Algebra and switching circuit. Retrieved http://poincare.matf.bg.ac.rs/~zarkom/Book_Shaums_BooleanAlgebraMendelson.pdf Levitz, K. and Levitz, H. (2016).Logic and Boolean algebra. Retrieved http://158.108.22.9/suchai/417231/logic_boolean.pdf