3. If the 5-bit 2's complement of X is equal to 10110, then without converting X to decimal, answer the following questions. a) What is the 5-bit 2's complement of -X? b) What is the 8-bit 2's complement of X? c) What is the 8-bit 2's complement of -X?
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- 1. Assume numbers are represented in 8-bit two's complement Show the calculation of the following: a) 5 + 10 b) 5 – 10 c) -5 + 10 d)-5 – 10 2. Represent the following decimal numbers or values according to the given requirements: a) +4 in both binary sign/magnitude and two's complement b) -6 in both binary sign/magnitude and two's complement c) -85 in two's complement d) +52 in two's complement 3. Find the following differences using twos complement arithmetic: a) 001000 – 110111 b) 10100101 – 011110 c) 100100001011 – 101010110011 d) 10011011 – 10100101Question 5 What is the largest number which can be encoded in the one's complement convention on a 16-bit machine? (You can use the character to denote taking a power of a number)Assume that we have two different computers. One has a word length of 6 bits and the other has a word length of 15 bits. A) What is the range of numbers that can be stored in these computers assuming that the stored data is unsigned (without the sign bit)? B) What is the range of numbers that can be stored in these computers assuming 1’s complement is used to store data? C) What is the range of numbers that can be stored in these computers assuming 2’s complement is used to store data?
- 9. Answer the following questions about IEEE 754 32-bit single precision numbers. a. Draw a diagram of the number format. b. What’s the range of numbers that can be represented? c. What’s meant by normalization? d. What’s the implied bit? e. What’s meant by exponent overflow and underflow? f. What’s meant by significand overflow and underflow? g. How’s + ∞ represented? h. How would he following numbers be represented? i. 1.6328125 x 2^-20 ii. 1.6328125 x 2^20 iii. -1.6328125 x 2^-20 iv. -1.6328125 x 2^20Are you able to differentiate between the least significant bit and the most significant bit in a given set of data?Please answer parts a, b, and c of this question. Assume we are using the simple model for floating-point representation as given in the text (the representation uses a 14-bit format, 5 bits for the exponent with a bias of 15, a normalized mantissa of 8 bits, and a single sign bit for the number): a) Show how the computer would represent the numbers 100.0 and 0.25 using this floating-point format. b) Show how the computer would add the two floating-point numbers in Part a by changing one of the numbers so they are both expressed using the same power of 2. c) Show how the computer would represent the sum in Part b using the given floating-point representation. What decimal value for the sum is the computer actually storing? Explain.
- Question 23 options: Using the rules of the simple floating point model (1-bit sign, 5-bit biased exponent, 8-bit significand, and normalized such that the leftmost bit of the significand is always 1), the number 8.4375 (decimal) can be expressed as: (Do not use spaces or any English text. Provide only 14 bits.)7. Add the following two 8-bit binary numbers, producing an 8-bit result. Indicate the status of the carry and overflow bits at the end of the addition by circling the appropriate choices. The space in between is only for readability. 1101 0110 + 1001 0111 -------------- Overflow? Yes or No Carry? Yes or Nodont use others answers 3 a) Represent the decimal number -89 in binary using 8-bit: i.Signed magnitude: ____________________________ ii.One's complement: ____________________________ iii.Two's complement: ___________________________ b) What decimal value does the 8-bit binary number 10011110 have if: i.it is interpreted as an unsigned number? ___________________________ ii.it is on a computer using signed-magnitude representation? _______________________ iii.it is on a computer using one’s complement representation? _______________________ iv.it is on a computer using two’s complement representation? _______________________
- Question5) Given Two Integers 11 and 9 how many binary bits are required to represent the larger one?A) Using the floating point format from number 2 (5 bit significand, 5 bit exponent), represent 47 as accurately as you can? B) What number is really represented and why? Can anyone answer these questions based on the the solution above.1. Suppose (27.625 base 10) is represented using a 16-bit Floating Point Format where 1 bit is for the sign bit, 5 bits is for exponent and 10 bits is for mantissa. What is the exponent? Do not involve a space character when you type your answer. 2. Suppose (-27.625 base 10) is represented using a 16-bit Floating Point Format where 1 bit is for the sign bit, 5 bits is for exponent and 10 bits is for mantissa. What is the the result? Do not involve a space character when you type your answer.