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
______________ 2 = ___________________8 ______________10 = _______________BCD
(a) Given the following Boolean expression
(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)
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
(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.
(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:
(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 :
(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
(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.
(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
(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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