Mumbai University > Computer Engineering > sem 4> Computer Organization and Architecture

Marks: 5M

Year: May16

Step 1: Convert the decimal number to its binary fractional form.

Convert this format is in base2 format For this, first convert 172 in to binary format

35=100011

Convert 0.25 in to binary format

0.25*2=0.50 0

0.50*2=1.0 1

0.25=10

Binary format of 35.25=100011.10

Shifting this binary number

1.00011102 *5 Normalized

1.0101100 is mantissa

2 **7 is exponent

add exponent 127 7+127=134

Step 2: Normalize the binary fractional number.

Move the decimal point left or right so that only a single binary digit "1" is to the left of the binary decimal point. Compensate by adjusting the exponent in the opposite direction.

1.0001110 times 2*5

Moving the decimal left seven decreases the size of the number; so, we use an exponent of 5 to compensate and keep the number the same size.

Step 3: Convert the exponent to 8-bit excess-127 notation

Add 127 to the exponent and convert it to 8-bit binary:

5 + 127 = 132--> 10000100

Step 4: Convert the mantissa/significand to "hidden bit" format.

Since every binary floating-point number (except zero!) is normalized with "1." at the start, there is no need to store that leftmost "1".

Remove the leading "1." from the mantissa/significand:

1.0001110 --> 0001110

Step 5: Write down the 1+8+23 = 32 bits.

35.25 is positive - the sign bit is zero: 0

The next eight bits are the exponent: 10000100

Binary result (32 bits): 0100001000011100000000000000000