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CSI VELLORE DIOCESE MATRIC. HR. SEC. SCHOOL, SIPCOT, RANIPET – 632 403., , Chapter 2 Number Systems, PART – 1, I. Choose The Correct Answer, Question 1., Which refers to the number of bits processed by a computer’s CPU?, (a) Byte, (b) Nibble, (c) Word length, (d) Bit, Answer:, (c) Word length, Question 2., How many bytes does 1 KiloByte contain?, (a) 1000, (b) 8, (c) 4, (d) 1024, Answer:, (d) 1024, , Question 3., Expansion for ASCII ……………….., (а) American School Code for Information Interchange, (b) American Standard Code for Information Interchange, (c) All Standard Code for Information Interchange, (d) American Society Code for Information Interchange, Answer:, (b) American Standard Code for Information Interchange, Question 4., 2^50 is referred as, (a) Kilo, (b) Tera, (c) Peta, (d) Zetta, Answer:, (c) Peta
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Question 5., How many characters can be handled in Binary Coded Decimal System?, (a) 64, (b) 255, (c) 256, (d) 128, Answer:, (a) 64, Question 6., For 11012 what is the Hexadecimal equivalent?, (a) F, (b) E, (c) D, (d) B, Answer:, (c) D, , Question 7., What is the 1’s complement of 00100110?, (a) 00100110, (b) 11011001, (c) 11010001, (d) 00101001, Answer:, (b) 11011001, Question 8., Which amongst this is not an Octal number?, (a) 645, (b) 234, (c) 876, (d) 123, Answer:, (c) 876, II. Short Answers, Question 1., What is data?, Answer:, The term data comes from the word datum which means a raw fact. The data is a fact, about people, places or some objects., Example: Rajesh, 16, XI
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Question 2., Write the 1’s complement procedure., Answer:, Step 1 : convert given decimal number into Binary, Step 2 : if the binary bit contains 8 bits if less add 0 at the left most bit, to make it as 8, bits., Step 3 : Invert all the bits, (i.e.) change 1 as 0 and 0 as 1., Question 3., Convert (46)10 into Binary number, Answer:, (46)10 into binary = 1011102, , Question 4., We cannot find 1’s complement for (28)10. State reason., Answer:, Since it is a positive number. 1 ’s complement will come only for negative number., Question 5., List the encoding systems for characters in memory., Answer:, 1. BCD – Binary Coded Decimal, 2. EBCDIC – Extended Binary Coded Decimal Interchange Code, 3. ASCII – American Standard Code for Information Interchange, 4. Unicode, 5. ISCII – Indian standard code for Information interchange, III. Explain in Brief, Question 1., What is radix of a number system? Give example., Answer:, The radix refers to the base of a number system: the total number of possible digits., The decimal number system that we all use is base ten, as it has ten distinct digits (0, 1,, 2, 3, 4, 5, 6, 7, 8, 9)., Example : Binary system – Radix 2, Question 2., Write note on binary number system., Answer:, In Binary Number System, there are only two digits namely 0 and 1. The numbers in the
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binary system are represented to the base 2. In the Binary Number, the left most bit is, the Most Significant Bit (MSB) and the right most bit is the Least Significant Bit (LSB)., MSB has largest positional weight and LSB has smallest positional weight., Example : 1100102, Question 3., Convert (150)10 into Binary, then convert that Binary number to Octal., Step 1:, Change it to Binary., , (150)10 = 10010110, Step – 2:, Change it to Octal., , Answer:, Binary 100101102, Octal 226g, Question 4., Write short note on ISCII., Answer:, ISCII – Indian Standard Code for Information Interchange (ISCII) is the system of, handling the character of Indian local languages. This is a 8 – bit coding system., Therefore it can handle 256 (28) characters. It is recognized by Bureau of Indian, Standards (BIS). It is integrated with Unicode., The supported scripts are:, Assamese, Bengali (Bangla), Devanagari, Gujarati, Gurmukhi, Kannada, Malayalam,, Oriya, Tamil, and Telugu. ISCII does not encode the writing systems of India based on, Arabic, but its writing system switching codes none the less provide for Kashmiri, Sindhi,, Urdu, Persian, Pashto and Arabic. The Arabic – based writing systems were subsequently, encoded in the PASCII encoding., ISCII is an 8 – bit encoding. The lower 128 code points are plain ASCII, the upper 128, code points are ISCII – specific. In addition to the code points representing characters,, ISCII makes use of a code point with mnemonic ATR that indicates that the following, byte contains one of two kinds of information. One set of values changes the writing, system until the next writing system indicator or end – of – line.
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Question 5., Add (a) – 2210 + 1510, (b) 2010 + 2510, , Answer:, , = 101102, Binary Equivalent = 101102, (a) – 2210, , Answer:, 111110012, , (b) 2010 + 2510, Answer:, , Answer:, 001011012
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IV. Detail Answers, Question 1., (a) Write the procedure to convert fractional Decimal to Binary., (b) Convert (98.46)10 to Binary, Answer:, (а) Procedure to convert fractional Decimal to Binary., Step 1 : Multiply the decimal fraction by 2 and note the integer part. The integer part is, either Oor 1., Step 2 : Discard the integer part of the previous product. Multiply the fractional part of, the previous product by 2. Repeat step 1 until the same fraction repeats or terminates, (0)., Step 3 : The resulting integer part forms a sequence of 0’s and 1 ’s that becomes the, binary equivalent of decimal fraction., Step 4 : The final answer is to be written from first integer part obtained till the last, integer part obtained., (b) Convert (98.46)10 to Binary, , Answer:, 1100010.01110 … 2, Question 2., Find 1’s Complement and 2’s Complement for the following Decimal number (a) – 98, (b) – 135, Answer:, , 9810 = 01100010, 8 bit format = 01100010, 1’s complement = 10011101, Add 1 bit = + 1
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= 10011110, , 13510 = 10000111, 1’st complement = 01111000, Add 1 bit = + 1, = 01111001, Question 3., (a) Add 11010102 + 1011012, (b) Subtract 11010112 – 1110102, Answer:, , PART – 1, I. Choose the correct answer, Question 1., Which is a basic electronic circuit which operates on one or more signals?, (a) Boolean algebra, (b) Gate, (c) Fundamental gates, (d) Derived gates, Answer:, (b) Gate, Question 2., Which gate is called as the logical inverter?, (a) AND, (b) OR, (c) NOT, (d) XNOR
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Answer:, (c) NOT, , Question 3., A+A=?, (a) A, (b) O, (c) 1, (d) A, Answer:, (a) A, Question 4., NOR is a combination of?, (a) NOT(OR), (b) NOT(AND), (c) NOT(NOT), (d) NOT(NOR), Answer:, (a) NOT(OR), Question 5., NAND is called as ……………… Gate., (a) Fundamental Gate, (b) Derived Gate, (c) Logical Gate, (d) Electronic gate, Answer:, (b) Derived Gate, PART – 2, II. Short Answers, Question 1., What is Boolean Algebra?, Answer:, Boolean algebra is a mathematical discipline that is used for designing digital circuits in, a digital computer. It describes the relation between inputs and outputs of a digital, circuit., Question 2., Write a short note on NAND Gate., Answer:
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The NAND gate is the combination of NOT and AND gates. The NAND gate is, generated by inverting the output of a AND gate. The algebraic expression of the, NAND is Y = A.B¯¯¯¯¯¯¯¯¯, Question 3., Draw the truth table for XOR gate., Answer:, The truth table for XOR gate is, , Question 4., Write the associative laws?, Answer:, A + (B + C) = (A + B) + C, A.(B.C) = (A.B).C, Question 5., What are derived gates?, Answer:, Derived Gates are the gates which are derived from the fundamental gates., Example : NAND, NOR, XOR, XNOR, PART – 3, III. Explain in Brief, Question 1., Write the truth table of fundamental gates., Answer:, (a) AND gate – Truth Table
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(b) OR gate – Truth Table, , (c) NOT Gate – Truth Table, , Question 2., Write a short note on XNOR gate., The XNOR (exclusive – NOR) gate is a combination of XOR gate followed by an inverter., Its output is “true” if the inputs are same and false if the inputs are different., The output of XNOR is C = AB + A¯¯¯¯ B¯¯¯¯, =A⊙B, Where ⊙ indicates included dot., Truth Table:, , Logic symbol:, , Logic circuit:, , Question 3., Reason out why the NAND an NOR are called universal gates?, Answer:, NAND and NOR gates are called as Universal gates because the fundamental logic, gates can be realized through them.
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Question 4., Give the truth table of XOR gate., Answer:, XOR – Truth Table, , Question 5., Write the De Morgan’s law., Answer:, De Morgan’s A+B¯¯¯¯¯¯¯¯¯¯¯¯¯¯ = A¯¯¯¯ . B¯¯¯¯, (A+B¯¯¯¯¯¯¯¯¯¯¯¯¯¯) = A¯¯¯¯ + B¯¯¯¯, PART – 4, IV. Explain in Detail, Question 1., Explain the fundamental gates with expression and truth table., Answer:, A gate is a basic electronic circuit which operates on one or more signals to produce an, output signal., The three fundamental gates are AND, OR and NOT gates., AND Gate:, The AND gate can have two or more input signals and produce an output signal. The, output is “true” only when both inputs are “true”, otherwise, the output is “false”. In, other words the output will be 1 if and only if both inputs are 1; otherwise the output is, 0. The output of the AND gate is represented by a variable say C, where A and B are two, and if input boolean variables. In boolean algebra, a variable can take either of the, values ‘0’ or ‘1’. The logical symbol of the AND gate is
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The truth table for AND gate is, , OR Gate:, The OR gate gets its name from its behaviour like the logical inclusive “OR”. The output, is “true” if either or both of the inputs are “true”. If both inputs are “false” then the, output is “false”. In other words the output will be 1 if and only if one or both inputs are, 1; otherwise, the output is 0. The logical symbol of the OR gate is, , The truth table for OR gate is, , NOT Gate:, The NOT gate, called a logical inverter, has only one input. It reverses the logical state., In other words the output C is always the complement of the input. The logical symbol, of the NOT gate is, , The truth table for NOT gate is, , Question 2., How AND and OR can be realized using NAND and NOR gate., Bubbled AND Gate
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(i) Realized of and using only AND gate:, The Boolean function for AND is C = AB. The same can be realized using only NAND, gates., , (ii) Realization of or using only NAND’s:, The Boolean function of OR is C = A + B. The same can be realized using only NAND, gates., , (iii) Realization of AND using NOR:, By using only the NOR gates, we can get the output equivalent to the output of AND, gate., C = A.B, , (iv) Realization of OR using NOR’s:
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By using only NOR gates we are getting the output equivalent to OR gate., , Question 3., Explain the Derived gates with expression and truth table., Answer:, The logic gates like NAND, NOR, XOR and XNOR are derived gates which are derived, from the fundamental gates AND, OR NOT., (i) NAND gate:, The NAND is the combination of NOT and AND. The NAND is generated by inverting, the output of an AND operation., Output: y = AB¯¯¯¯¯¯¯, Logic circuit, , Logic symbol:, , Truth table:, , Inputs Outputs, (ii) NOR gate:, The NOR is the combination of NOT and OR. The NOR is generated by inverting the, output of an OR operation., Logic function: y = AB¯¯¯¯¯¯¯, Logic circuit:
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logic symbol:, , Truth table:, , (iii) XOR gate:, The XOR (exclusive – OR) gate acts in the same way as the logical either /or., Logic symbol:, , Logic circuit:, , Truth table:, , (iv) XNOR gate:, XNOR gate (exclusive – NOR) gate is a combination of XOR gate followed by an, inverter.
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Logic function: y = AB¯¯¯¯¯¯¯, , logic symbol:, , Truth table:, , Boolean function:, , **************** ALL THE BEST *****************
