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## CS101 ASSIGNMENT 1 SOLUTION FALL 2021

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Total Marks: 20

Due Date: 14 Dec 2021

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Objectives:

1. To understand the practical implementation of the Number System and learn how to convert numbers from decimal to binary or binary to decimal.

2. To understand the concept of Addition in binary Boolean Logical Operations.

3. To understand the basic concept of Boolean Logical Operations.

Question 1:

Hint: Use the following 8-bit floating-point notation to convert these values.

Part A:

Encode the following decimal fractional value to binary floating-point notation using the 8-bit floating-point format.

-3.5

Solution:

The number is negative so sign bit notation is 1. o First convert 3.5 into a Binary of 3.5

3.5 = 011.1

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Mantissa field: 0111 radix in .0111 must be moved 3-bit to the right to obtain 011.1 So exponent is positive 3

The final 8-bit floating-point notation is

3.5 decimal fractional value is using 8-bit floating-point notation is -11110111

Part B:

Decode the following 8-bit floating point binary value to decimal fractional value.

00101100

Solution:

The mantissa is: .1100

Exponent: 010 It is in 3-bit excess notation-4

-2 Exponent is negative so shift radix (.1100) left.

001100 Convert it into decimal fractional value .001100 is equal to .0011.

0 + 0 + 1/8 + 1/6

=0.1875

Question 2:

Perform the binary addition on the following decimal numbers:

4638 and 9278

Solution:

Convert into binary

4638=101110.0110

9278=1011100.1110

Perform addition

1+0=1

1+1=0 (1 carry)

1+1+1=1(1 carry)

0+1=1

=10001011.0100

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Question 3:

The logical operations (AND, OR, NOT, and XOR etc.) discussed in the video lessons can be combined to perform some specific operations. Two such operations (circuits) are depicted in the first column “Circuits” of the following table. You are required to determine the output of each of the following circuits for the input values given in column 2 and column 3.

Solution:

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