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CS101 ASSIGNMENT 1 SOLUTION 2021 | CS101 ASSIGNMENT 1 FALL 2021 | CS101 ASSIGNMENT 1 2021 | INTRODUCTION TO COMPUTING I VuTech

CS101 ASSIGNMENT 1 SOLUTION 2021 | CS101 ASSIGNMENT 1 FALL 2021 | CS101 ASSIGNMENT 1 2021 | INTRODUCTION TO COMPUTING I VuTech

CS101 ASSIGNMENT 1 SOLUTION 2021 | CS101 ASSIGNMENT 1 FALL 2021 | CS101 ASSIGNMENT 1 2021 | INTRODUCTION TO COMPUTING I VuTech

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Question No. 1

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


{ -3.5}


As the number is negative so the sign bit of floating-point notation is 1

We convert 3.5 into binary

Binary of 3.5 is 011.1

Mantissa field is 0111

We see that the radix in .0111 must be moved 3 bits to the right to obtain

011.1

So, exponent is positive 3 (in excess notation-4 is 111)

The final 8 bit floating point notation is 

1

1

1

1

0

1

1

1


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

00101100

 

0

0

1

0

1

1

0

0

 

 

Our Mantissa is

.1100

Exponent

010

It is in 3-bit excess notation-4:

-2

Exponent is negative so shift radix of (.1100) towards the left

 

.001100

 

Convert it into decimal fractional value

 

.001100 is equal to .0011

 

.

2-1

2-2

2-3

2-4

.

1/2

¼

1/8

1/16

.

0

0

1

1

 

0+0+1/8+1/16=0.1875 Answer

 

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

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Questions No. 2

Perform the binary addition on the following decimal numbers and 92

 

Convert into binary


=101110.0110

 

92 1011100.1110

Perform addition

 

1+0=1

1+1=0 (1 carry)

1+1+1=1(1 carry)

0+1=1

 

 

1

0

1

1

1

0

0

.

1

1

1

 

0

1

0

1

1

1

0

.

0

1

1

 

 

 

 

 

 

 

 

 

 

 

+

1

0

0

0

1

0

1

1

.

0

1

0

 

So,

10001011.010 Answer


Questions No. 3

The logical operations (AND, OR, NOT, 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 columns 2 and column 3.

 

 

Circuits

What would be the output when the upper input is 1 and the lower input is 0?

What would be the output when the upper input is 0 and the lower input is 1?

 

 

 

INPUTS                               OUTPUT

0

0

 

 

INPUTS                               OUTPUT

0

1

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