Write down the binary bit pattern assuming a format similar to that employed by the DEC PDP-8 (the leftmost 12 bits are the exponent stored as a two’s complement number, and the rightmost 24 bits are the mantissa stored as a two’s complement number ). No hidden 1 is used. Comment on how the range and accuracy of this 36-bit pattern compares to the single and double precision IEEE 754 standards.

In the IEEE 754 floating point standard the exponent is stored in "bias" (also known as "Excess-N") format. This approach was selected because we want an all-zero pattern to be as close to zero as possible. Because of the use of a hidden 1, if we were to represent the exponent in two's complement format an all-zero pattern would actually be the number 1! (Remember, anything raised to the zeroth power is 1, so 1.0⁰ = 1.) There are many other aspects of the IEEE 754 standard that exist in order to help hardware loating point units work more quickly. However, in many older machines loating point calculations were handled in software, and therefore other formats were used. The following table shows decimal numbers.

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a. b. -1.5625 x 10-1¹ 9.356875 x 10²