Machine Structure & Assembly Programming Language (Computer Science)

(2) [10 points] While representing negative integer why do we prefer to use 2s complement format instead of either direct negative numbers (i.e., sign-magnitude format) or 1s complement format. Explain.

(3) [5 points] What decimal number does the (stored or,) IEEE 754 standard based bit pattern 0C000000 with base of 16 represent 10 based floating point number? Explain.

(4) [5+5 =10] Write down the (stored or,) IEEE 754 binary representation of the decimal number 63.2510 in (a) IEEE 754 single precision format, (b) and in IEEE 754 double precision format. Explain.

(5) [4 + 8 = 12] IEEE 754-2008 contains a half precision that it is only 16 bits wide. The leftmost bit is still the sign bit, the exponent is 5 bits wide and has a bias of 15, and the mantissa is 10 bits long. (a) Write down the (binary) bit pattern to represent 1.5625101. Show all steps. (b) Calculate the sum of 2.6125101 and 4.150390625101 assuming A and B are stored in the 16- bit half precision of IEEE 754-2008. You must show all the steps.

(6) [5 + 5 + 5 + (3 + 10) = 28] In IEEE 754 64 bit (double precision), what is the minimum positive

(a) normal number as well as the (b) de-normal number (but non-zero) we can represent. (c) What is the maximum number (but non-infinity) we can present in this format? (d) From (b) and (c) you can see the range of magnitude possible within these 64 bit

numbers. (i) Is this range larger than 2^64 signed integer range? (ii) If not then why not if yes then why it is so, explain. After all both can only present 2^64 possible numbers.