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Logic

Design

Subject Code : BT0064

Student Name : Zainab

Roll Number :

Course : BScIT Semester – I

Assignment : BT0064 (Logic Design)

Learning Center Name: Global Institute for Management Science

Learning Center Code : 02519

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Date of Submission : ________________________

Marks Awarded : ________________________

Remarks : ____________________________________

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Zainab

BScIT – Semester 1

BT0064 – Logic Design – 4 Credits

Assignment Set – 1

Answer all questions:

1. Convert the following octal numbers to base 10:

a) 273 - 187

b) 1021- 529

2. Convert the following decimal numbers to base 2:

a) 122 - 1111010

b) 98 - 1100010

3. List out the fundamental logical gates.

A: The inverter, which returns the reverse of the input. The AND gate which returns a high output if and only if both inputs are high. The OR gate, which returns a high output if either or both inputs are high. The NAND and NOR gates return the opposite of their counterparts. They are basically the AND and OR gates with an inverter after them. The XOR gate is the exclusive OR gate; it returns a high output it either input is high, but not both. Every binary combination of outputs can be made from these operators. In fact, you don't even need all of them. The NAND and the NOR gate can both create every other gate.

4. How can you realize AND gate using NOR gate?

A: A 2 input AND gate can be realized by using 3 NOR gates as follows:

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|Input |Output |

|A |B |Y |

|0 |0 |0 |

|0 |1 |1 |

|1 |0 |1 |

|1 |1 |1 |

5. Simplify the following three-variable Boolean functions algebraically:

a) f1 = Σ1, 2, 5, 6

|A\BC |B’C’ |B’C |BC |BC’ |

|A’ | |1 | |1 |

|A | |1 | |1 |

f1 = A’B’C + AB’C + A’BC’ + ABC’

= B’C(A’ + A) + BC’(A’ + A)

= B’C + BC’ = 1

b) f2 = Σ1, 2, 3, 7

|A\BC |B’C’ |B’C |BC |BC’ |

|A’ | |1 |1 |1 |

|A | | |1 | |

f2 = A’B’C + A’BC + A’BC + A’BC’ + A’BC + ABC

= A’C(B’ + B) + A’B(C + C’) + BC(A’ + A)

= A’C + A’B + BC

6. Minimize the following functions using Quine-McCluskey tabular method:

a) ƒ(A,B,C,D) = ∑0,1,3,6,9,10,11,12,14,15

b) ƒ(A,B,C,D,E) = ∑0,1,5,8,11,12,14,16,20,21,25,27,28,30,31(with don’t care terms 2,7,13,22,23)

A: a) ƒ =  A'B'C' + B'D + BCD' + AC + ABD'

b)ƒ =  ACD + B'CE + A'B'D'E + A'C'D'E' + AB'D'E' + BC'DE + BCE' +

ABC'E

7. What is Multiplexer? Draw the logic diagram 8 to 1 line multiplexer.

A: In electronics, a multiplexer (or MUX) is a device that selects one of several analog or digital input signals and forwards the selected input into a single line. A multiplexer of 2n inputs has n select lines, which are used to select which input line to send to the output. Multiplexers are mainly used to increase the amount of data that can be sent over the network within a certain amount of time and bandwidth. A multiplexer is also called a data selector. They are used in CCTV, and almost every business that has CCTV fitted, will own one of these.

An electronic multiplexer makes it possible for several signals to share one device or resource, for example one A/D converter or one communication line, instead of having one device per input signal.

An electronic multiplexer can be considered as a multiple-input, single-output switch, and the schematic symbol for a multiplexer is an isosceles trapezoid with the longer parallel side containing the input pins and the short parallel side containing the output pin.

The logic diagram below shows an 8 to 1 line multiplexer:

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8. What is a comparator? Design the combinational circuit that will compare two bits A and B and produce 3 outputs A>B, A=B, A ................
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