CS101 Assignment 1 Fall 2021

CS101 Assignment Solution # 1 Fall 2021

Q1. PART A:

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

Solution:

o -3.5 As number is negative so sign bit notation is 1. o First convert 3.5 into binary Binary of 3.5 is 011.1

Mantissa field: 0111 radix in .0111 must be moved 3 bit to the right to obtain

11. 1

So exponent is positive 3…

Final 8 bit floating point notation is

PART B:

Decode the following 8-bit floating point binary value to decimal fractional value. Convert into binary 46(3/8)=101110.0110 92(7/8)=1011100.1110

Now, 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.