Question

Write down the bit pattern in the fraction assuming a floating-point format that uses Binary Coded Decimal (base 10) numbers in the fraction instead of base 2. Assume there are 24 bits, and you do not need to normalize. Is this representation exact?

Short answer

The value is 0011 0011 0011 0011 0011 0011 and it is not exact.

Step-by-step solution

Determine the floating-point format and BCD.

The value of the fraction will be the number with a decimal point. The number will be converted to a binary number. The binary coded decimal numbers are with the base 10 in the fraction format. Each decimal value will have a corresponding binary code, which will be presented without any conversions

Determine the bit pattern of the fraction value 1/3 as BCD.

The given number is 1/3.

The decimal value of the given number is 0.333333.

The above number can be written as

Now, converting the number to its BCD, we have

333333 = 0011 0011 0011 0011 0011 0011

The above value is not exact because the value does not represent the exponent and it is not normalized