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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:**

**D****ecode the following 8-bit floating point binary value to decimal fractional**** ****value.**

**0****0101100**

**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**

2^{5}^{} | 2^{4}^{} | 2^{3}^{} | 2^{2}^{} | 2^{1}^{} | 2^{0}^{} |

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

2^{6}^{} | 2^{5}^{} | 2^{4}^{} | 2^{3}^{} | 2^{2}^{} | 2^{1}^{} | 2^{0}^{} |

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:**

**D****ecode the following 8-bit floating point binary value to decimal fractional**** ****value.**

**0****0101100**

**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**

2^{5}^{} | 2^{4}^{} | 2^{3}^{} | 2^{2}^{} | 2^{1}^{} | 2^{0}^{} |

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

2^{6}^{} | 2^{5}^{} | 2^{4}^{} | 2^{3}^{} | 2^{2}^{} | 2^{1}^{} | 2^{0}^{} |

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