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CS101 Assignment 1 Solution Fall 2021 Perfect Solution
Question No 1
- Encode the following decimal fractional value to binary floating point notation using the 8-bit floating-point format.
- -3.5
- Decode the following 8-bit floating point binary value to decimal fractional value.
- 00101100
Hint: Use the following 8-bit floating-point notation to convert these values.
Solution:
PART A:
Step 1:
As the given Number is negative that’s why Sign bit of Floating point notation will be 1
Step : 2
Now we will Convert 3.5 Decimal Number into Binary One.
| 2 | 2 | 2 | Redix | 2 |
| 4 | 2 | 1 | 1/2 | |
| 0 | 1 | 1 | . | 1 |
3.5 in a Binary One is 011.1
Find Mantisa:
To Get the Mantisa, we must have to move 3 numbers towards right side in the concluded binary number that is 011.1.
And after moving:
.0111
So, our Exponent is Positive 3 in excess notation 4 is 111
Our Final 8 bit floating Notation is
11110111
PART B:
Decode the following 8-bit floating point binary value to decimal fractional value.
00101100
Solution:
FOR MANTISA:
Using the strategy of dividing the given number in four bit pattern then Our Mantisa will be:
1100
FOR EXPONENT:
Our Exponent is 010
And in 3 bit Excess notation 010 is equal to -2.
Our Exponent is Negative that’s why we will shift our redix of .1100 towards the left Side.
Then we will get the below given result;
.101100
Now we will convert the given Binary value into Decimal value.
.101100 is equal to 1011.
| . | 2-1 | 2-2 | 2-3 | 2-4 |
| . | 1/2 | 1/4 | 1/8 | 1/16 |
| 1 | 0 | 1 | 1 |
1/2 + 0 + 1/8 + 1/16 =
8 + 2 + 1 / 16 = 11/16
= 0.6875 Answer
Perform the binary addition on the following decimal numbers:
46 3
8
and 92 7
8
Solution:
As we have given data and Now we will convert this decimal data into binary addition but one by one:
PART 1:
46 3/8
| 25 | 24 | 23 | 22 | 21 | 20 |
| 32 | 16 | 8 | 4 | 2 | 1 |
| 1 | 0 | 1 | 1 | 1 | 0 |
And Redix:
| 2-1 | 2-2 | 2-3 | 2-4 |
| 1/2 | 1/4 | 1/8 | 1/16 |
| 0 | 1 | 1 | 0 |
PART 2
92 7/8
| 26 | 25 | 24 | 23 | 22 | 21 | 20 |
| 64 | 32 | 16 | 8 | 4 | 2 | 1 |
| 1 | 1 | 0 | 1 | 1 | 1 | 0 |
And Redix:
| 2-1 | 2-2 | 2-3 | 2-4 |
| 1/2 | 1/4 | 1/8 | 1/16 |
| 1 | 1 | 1 | 0 |
Now Part One in Binary Digit is 101110.0110
While Part Two in Binary Digit is 1011100.1110
Now we will add these Binary Numbers:
Addition:
| 1 | 0 | 1 | 1 | 1 | 0 | 0 | . | 1 | 1 | 1 | 0 | |
| 0 | 1 | 0 | 1 | 1 | 1 | 0 | . | 0 | 1 | 1 | 0 | |
| + | ||||||||||||
| 1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 |
So we Got the Final Binary Number
Answer is 10001011.0100
Question Number 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 upper input is 0 and the lower input is 1? |
| A | 0 | 0 |
| B | 0 | 1 |
CS101 Assignment 1 Solution Fall 2021
By ConceptsBuilder
Question No 1
- Encode the following decimal fractional value to binary floating point notation using the 8-bit floating-point format.
- -3.5
- Decode the following 8-bit floating point binary value to decimal fractional value.
- 00101100
Hint: Use the following 8-bit floating-point notation to convert these values.
Solution:
PART A:
Step 1:
As the given Number is negative that’s why Sign bit of Floating point notation will be 1
Step : 2
Now we will Convert 3.5 Decimal Number into Binary One.
| 2 | 2 | 2 | Redix | 2 |
| 4 | 2 | 1 | 1/2 | |
| 0 | 1 | 1 | . | 1 |
3.5 in a Binary One is 011.1
Find Mantisa:
To Get the Mantisa, we must have to move 3 numbers towards right side in the concluded binary number that is 011.1.
And after moving:
.0111
So, our Exponent is Positive 3 in excess notation 4 is 111
Our Final 8 bit floating Notation is
11110111
PART B:
Decode the following 8-bit floating point binary value to decimal fractional value.
00101100
Solution:
FOR MANTISA:
Using the strategy of dividing the given number in four bit pattern then Our Mantisa will be:
1100
FOR EXPONENT:
Our Exponent is 010
And in 3 bit Excess notation 010 is equal to -2.
Our Exponent is Negative that’s why we will shift our redix of .1100 towards the left Side.
Then we will get the below given result;
.101100
Now we will convert the given Binary value into Decimal value.
.101100 is equal to 1011.
| . | 2-1 | 2-2 | 2-3 | 2-4 |
| . | 1/2 | 1/4 | 1/8 | 1/16 |
| 1 | 0 | 1 | 1 |
1/2 + 0 + 1/8 + 1/16 =
8 + 2 + 1 / 16 = 11/16
= 0.6875 Answer
Perform the binary addition on the following decimal numbers:
46 3
8
and 92 7
8
Solution:
As we have given data and Now we will convert this decimal data into binary addition but one by one:
PART 1:
46 3/8
| 25 | 24 | 23 | 22 | 21 | 20 |
| 32 | 16 | 8 | 4 | 2 | 1 |
| 1 | 0 | 1 | 1 | 1 | 0 |
And Redix:
| 2-1 | 2-2 | 2-3 | 2-4 |
| 1/2 | 1/4 | 1/8 | 1/16 |
| 0 | 1 | 1 | 0 |
PART 2
92 7/8
| 26 | 25 | 24 | 23 | 22 | 21 | 20 |
| 64 | 32 | 16 | 8 | 4 | 2 | 1 |
| 1 | 1 | 0 | 1 | 1 | 1 | 0 |
And Redix:
| 2-1 | 2-2 | 2-3 | 2-4 |
| 1/2 | 1/4 | 1/8 | 1/16 |
| 1 | 1 | 1 | 0 |
Now Part One in Binary Digit is 101110.0110
While Part Two in Binary Digit is 1011100.1110
Now we will add these Binary Numbers:
Addition:
| 1 | 0 | 1 | 1 | 1 | 0 | 0 | . | 1 | 1 | 1 | 0 | |
| 0 | 1 | 0 | 1 | 1 | 1 | 0 | . | 0 | 1 | 1 | 0 | |
| + | ||||||||||||
| 1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 |
So we Got the Final Binary Number
Answer is 10001011.0100
Question Number 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 upper input is 0 and the lower input is 1? |
| A | 0 | 0 |
| B | 0 | 1 |
CS101 Assignment 1 Solution Fall 2021 Perfect Solution
