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The IEEE Standard 754 representation of a floating point number
is given as: 01101110110011010100000000000000. Determine the
binary value represented by this number.
If a computer’s system clock is 2.4 GHz, calculate the period of the
system clock.
If an 8-bit binary number is used to represent an analog value in
the range from 200 ounces to 700 ounces, what is the resolution of
the system?
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- In a given 32-bit floating-point representation of numbers, if the number of bits of the mantissa is reduced to accommodate an increase in the number of bits of the exponent, this will result in the following: (select the best answer) Increased range of the numbers at the expense of the precision Increased precision of the numbers at the expense of the range Both range and precision increase Both range and precision decreaseRepresent the binary representation of a float type to integer type. Single precision float (32-bit length) is represented in IEEE754 format: 1 bit of sign, 8 for exponent plus bias of 127, and 23 for the mantissa. Example: * 85.125 is [101 0101.001] in binary and this would be [1.0101 0100 1 x 2^6] in scientific notation of base 2. * Our sign bit will be [0] (positive), exponent+bias is [1000 0101] (6 + 127 = 133), and mantissa of [0 1010 1001000...] (whole is omitted and zeroes are added to the right until its length is 23). * Merging this will be [0100 0010 1010 1010 0100 0000 0000 0000] which is equivalent as 1118453760 in integer. * Therefore, binary of 85.125 in float is 1118453760 in integer. Input A single line containing a float type non-positive number. 85.125Output A single line containing the integer representation of float type binary. 1118453760Scenario: In a biased N-bit binary number system with bias B, positive and negative numbers are represented as their value plus the bias B. For example, for 5-bit numbers with a bias of 15, the number 0 is represented as 01111, 1 as 10000, and so forth. Biased number systems are sometimes used in floating point mathematics. Consider a biased 8-bit binary number system with a bias of 12710 Question: What is the representation and value of the most negative number?
- In a Digital Logic examination, you are given two signed integers in different number systems. A= (64)16 B= -(103)8Determine their values in the decimal system AN, b) Find the value of n, the shortest word-length of a computer using two’s complement representation which can represent all these numbers. Find the largest and thesmallest numbers that can be represented. c) Give the n-bit two’s complement representations of the two numbers, where n isvalue determined in b.a) A fixed-point binary number system has 5 whole bits and 3 fractional bits. What is the range of numbers in binary that can be represented in this format? What is the decimal value of the largest number that can be represented? b) A fixed-point binary number system has 4 whole bits and 12 fractional bits. Show the (4-hexit) hexadecimal representation of the following decimal numbers 0.375, - 1.33, and 1/40 in this finite format. Do not show recurring sequences. c) Assume a 16-bit floating point format designed as follows: 4-bit signed exponent and 12-bit fraction. Normalization is strictly enforced. What is the hexadecimal representation of the 16-bit floating point format for 1/40?Consider the following floating point representation where each number has 2exponent bits and 5 fraction bits. The exponent bias is 1. Round each number tohave 3 fraction bits. Apply round-to-even and round-toward-zero modes.a. 1 10 11100b. 0 00 00101c. 1 01 10101i. Can you see a pattern for rounding floating point numbers when thenumber of exponent bits are intact?
- *All parts please* 2. (50 points) Binary Integer Arithmetic (a) (15 points) Given A = 1111 0011 1100 0011 1100 0000 0000 00002 and assuming A is a single precision IEEE-754 floating point number, what decimal value does A represent? Show A in normalized scientific notation: 1.X ∗ 2^Y. (b) (15 points) Convert 28.410 to IEEE-754 single-precision binary. (c) (20 points) Given X = 0100 0001 0110 1110 0000 0000 0000 00002 and Y = 0100 0001 1011 1100 0000 0000 0000 00002 in single precision IEEE-754 floating point numbers, perform the following operations. Show all your work and express the final answer in single precision IEEE 754-floating point representation. 1. X+Y 2. X*Y Hint: show each value in binary normalized scientific notation prior to performing the arithmetic. This should make following the algorithms easier.You are asked to design a 16-bit floating point number system to store the lengths of various man-made objects. This system should work in a similar way as the IEEE754 standard. Assume a value stored in the system denotes the length of an object in centimeters, assume also that the maximum length to be stored is 45845.0 centimeters (i.e. length of the biggest man-made oil-tanker, the “Seawise Giant”). Note: This representation has normalized, de-normalized and special cases as you have seen in IEEE754 standard. Answer the questions below: a) Is sign bit needed in this system? Why yes or why not. b) What is the minimum number of bits needed for the exponent? What is the value of the corresponding bias? Show your steps clearly. If you write the values directly without showing the steps, you will not get any point. c) What is the maximum length the system can represent? Please show your steps clearly, otherwise no point will be given.n alternative to hexadecimal notation for representing bit patterns is dotted decimal notation in which each byte in the pattern is represented by its base ten equivalent. In turn, these byte representations are separated by periods. For example, 12.5 represents the pattern 0000110000000101 (the byte 00001100 is represented by 12, and 00000101 is represented by 5), and the pattern 100010000001000000000111 is represented by 136.16.7. Represent each of the following bit patterns in dotted decimal notation. 0000111100001111 001100110000000010000000 0000101010100000
- A machine stores floating point number in a (1 + 1 + 3 + 6) -bit word. The first bit is for the sign of the number, the second bit is for the sign of the exponent, the next 3 bits are for the exponent, and the final 6 bits are for the mantissa. The machine epsilon for this approximation isLet B = 1(0 ∪ 1)* over Σ = {0, 1} be the language of positive binary integers.Provide a transducer that computes {y : y = 6x; x, y ∈ B}(a) Use BCD arithmetic to perform the calculation:14326 + 92378(b) In a particular computer numbers are stored in IEEE standard 754 floating point format, with an 8-bit mantissa and a 4-bit exponent.(i) Show how 43.125 would be stored (ii) What number is stored as 1 11001010 1011?