6_ConversionPractice_updated_9_11_2023

CNIT 17600 - Intro Computer Architecture - Conversion Practice 3 Question 3 In a computer system that represents all integer quantities using two’s complement form, the most significant bit has a negative place-weight. For an eight-bit system, the place weights are as follows: − 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 Given this place-weighting, convert the following eight-bit two’s complement binary num- bers into decimal form: 01110100 2 = 11010110 2 = 11111000 2 = 10101000 2 = 10000110 2 = 01110100 2 = 11111011 2 =

CNIT 17600 - Intro Computer Architecture - Conversion Practice 6 Question 5 Remember that a number system is a set of counting rules. When we are working within a number system (bound by the rules of which numerals are legal), there are generalizations we can make and patterns we can find. How is the base represented in each of the number systems? 2 10 in base 2? 8 10 in base 8? 16 10 in base 16? Question 6 Searching for patterns in numbers. Using your counting practice table as a source of pre- liminary data, draw generalized conclusions that can help speed up conversion between bases. Generate at least 4 data points for each sub question. –In base 10, how are multiples of the base represented? 2 · 10 10 =? 10 3 · 10 10 =? 10 4 · 10 10 =? 10 5 · 10 10 =? 10 –In base 2, how are multiples of the base represented? 2 · 2 10 =? 2 3 · 2 10 =? 2 4 · 2 10 =? 2 5 · 2 10 =? 2 –In base 8, how are multiples of the base represented? 2 · 8 10 =? 8 3 · 8 10 =? 8 4 · 8 10 =? 8 5 · 8 10 =? 8 –In base 16, how are multiples of the base represented? 2 · 16 10 =? 16 3 · 16 10 =? 16 4 · 16 10 =? 16 5 · 16 10 =? 16