# DD ASIMENT 2 - Q NO.1 What is a logic gate ANSWER The...

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Q NO.1: What is a logic gate? .
Q NO.2: Develop a circuit that produces 0 when all of its three input are 1 and 0 otherwise
F = (A + B ) = AB Q NO.8:  Find the value of x in the following a) (835)10=(X) BCD b) (EFCB) 16 = (x) 8 c) (12.354)10 = (X)2 d) (BEE)x = (2699)10 a) (835) 10 = (X) BCD SOLUTION: BCD = BINARY CODED DECIMAL ( 8 3 5 ) 10 ( 1000 0011 0101 ) BCD SO X = 100000110101 b) (EFCB) 16 = (x) 8 SOLUTION: ( E F C B ) 16 ( 1110 1111 1100 1011 ) 2 = ( 001 110 111 111 001 011 ) 2 = ( 1 6 7 7 1 3 ) 8 S0 X = 167713 c) (12.354) 10 = (X) 2 SOLUTION: 2 12 2 6 - 0 2 3 - 0 2 1 - 1 The binary equivalent is 1100. Then convert the fraction: AND GATE INPUTS OUTPUT X Y F 0 0 0 0 1 0 1 0 0 1 1 1
Integer Fraction Coefficient 0.354 2 = 0 . 708 0 0.708 2 = 1 . 416 1 0.416 2 = 0 . 832 0 The binary equivalent is .010 Hence, 12.354 is equivalent to binary 1100.010 SO, X = 1100.010 d) (BEE)x = (2699) 10 SOLUTION: B X 2 + E X 1 + E X 0 = 11X 2 + 14X + 14 = 2699 Thus,11X 2 + 14X- 2685 = 0 The above isa quadratic equation in X. X = -b  b 2 – 4ac 2a X = -14  (14) 2 – 4(11)(-2685) 2(11) X = -14  196 +118140 2(11) X = -14  118336 2(11) X = -14 344 2(11) X = -14+ 344 22 X = 330 22 X = 15 Q NO.9: Simplify the following boolean functions using K-maps. F (A, B, C) = ∑ (0,2,3,4,6)
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