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QUESTIONS 1 Do the following number conversions: All steps should be shown clearly. ( 5 marks ) (i) 325.525 10 (ii) 7565.3510 (iii) AB57.E2 H = (iv) E9B2.C4 H = (v) 7540. 75 8 = = = ________________ 2 ___________________ 8 ______________10 ______________ 2 = ___________________8 ______________10 = _______________BCD 2 (a) Given the following Boolean expression (i) Writethetruthtable. (ii) Simplify the Boolean expression using K-map. (iii)Draw the logic circuit after simplification using gates. ( 3 marks ) (b) For the given truth table, derive the standard SOP and standard POS expressions relating output X and inputs A, B, C and D. Write the answers both as a function of input variables and as a short form using numbers. (1⁄2 x4= 2Marks) 3 Do the following binary arithmetic : (i) Add the two Binary numbers : 11011.11 + 111010.0111 (ii) Add the four binary numbers : 1100+1101+1101+1110 (iii)Subtract the Binary numbers : 101010100. 010 – 1011001 . 011 (iv)Multiply 25 .5 by 8.5 in binary form (v) Perform the binary division : 10110100 ÷ 101 4 (a) Express the following decimal numbers as signed binary numbers : (i) + 758 in signed 1’s complement format (ii) – 58 in sign-magnitude format (iii) –98 in signed 2’s complement format . (b) Represent the decimal number 435689 in BCD format and calculate how many nibbles are there in this BCD number. (c) A typical CD-ROM contains 700 Megabytes of digital data. Express this value in bits. 5 (a) Write the simplified expression for X and give its truth table (b) Write the expression for the output X and develop a truth table for the circuit below: 6 (a) Simplify the following Boolean expression and draw a logic circuit for the simplified expression : (b) Get the expression for the output for the following logic circuit : 7 (a) Write the logic expression for the output X and obtain a truth table for the circuit shown below : By observing the table, explain what function is performed by this circuit. Which logic gate that you have studied, has a truth table similar to that of this circuit ? (b) Simplify the following Boolean expression 8 (a) X and Y are the two keys of a Locker. The Locker will be opened only when the two keys are both turned ON. Draw a logic gate that can do the above operation and write its truth table. ( 2 marks ) (b) A TV set (T) is kept in the main hall of the house. It should be switched ON and OFF through 4 switches A, B, C & D kept at different places. The TV should become ON only when a minimum of three switches are ON. In all other conditions, the TV should be ‘OFF’. (i) Draw a truth table with A,B,C, D as input and T as output to achieve this condition (ii)Get an expression for T in terms of A, B, C and D from the truth table and simplify the expression using a K Map. 9 (a) (b) Obtain a standard SOP expression for X (using their short form representation) In the circuit shown in the figure, if C = 0, find the simplified expression for Y 10 (a) Simplify the Boolean expression using K-map (b) Four inputs A, B, C, D are fed to logic circuit, which produces an output Y which operate a relay. The relay turns on when Y = 1 for the inputs(ABCD): ‘0000’, ‘0001’, ‘0100’, ‘0101’,‘0110’, ‘0111’, ‘1001’, ‘1011’ and ‘1111’. Further the inputs ‘1010’ and ‘1110’ can be treated as don’t cares (d). For the remaining states, the relay is off. ( Y = 0) (i) Draw a Truth table for this condition and write an expression for Y. (ii) Draw a K map for this condition, and simplify the expression.

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