Question

Question : 3.28 [20] The Hewlett-Packard 2114, 2115, and 2116 used a format with the left most 16 bits being the fraction stored in two’s complement format, followed by another 16-bit field which had the left most 8 bits as an extension of the fraction (making the fraction 24 bits long), and the rightmost 8 bits representing the exponent. However, in an interesting twist, the exponent was stored in sign-magnitude format with the sign bit on the far right! Write down the bit pattern to represent assuming this format. No hidden 1 is used. Comment on how the range and accuracy of this 32-bit pattern compares to the single precision IEEE 754 standards.

Short answer

The required result will be 10110000000000000000000000000101.

Step-by-step solution

Define the concept.

The decimal number system uses base 10 and the binary number system uses base 2.

For example, “12” is also equivalent to the value of the binary number system “1100”.

In the IEEE 754 single-precision format,

Determine the calculation.

In the decimal number system, -0.15625 is equivalent to the binary number

= -0.00101

Hence, the exponent will be -2.

And the fraction = -0.1010000000000000000000000000

Hence, the desired answer will be 10110000000000000000000000000101.