What is 7/3 as a normal-form, binary fraction?
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What is 7/3 as a normal-form, binary fraction?
a. 1.00101010…×2^−1
b. 10.0101010…×2^1
c. 10.0101010…×2^−1
d. 1.00101010…×2^1
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- 1. Find the binary code of the integer 97. 2. Find the binary code of the integer 89. 3. Find the decimal code of the binary number 01011010 4. Find the decimal code of the number 10010111.A. Add the two pairs of binary numbers X = 00101 and Y = 10111and show the results in binary. (Be sure to show the carry as you add.) Let us the call the result Z = X +Y. Carries 0010 1 (X) + 10111 (Y) (Z) B. Convert the binary integer 1010101011 to decimal. C. Convert decimal integer 1393 to binary. Show all your work, quotients, and remainders, and then write down the answer. D. Convert decimal integer 1393 to hexadecimal. You can use the answer from part (C) or could use calculator to do division. Show you work either way.2. Constrained by the size of the register in your old personal computer at home, youdecide to build a computer with a larger floating point register called R. Five octitscan be represented in R. You decide on the following format for the representation offloating point numbers:R: sign characteristic mantissaYou have available a 1 octit characteristic and a 3 octit mantissa.(b) Write the following decimal numbers as they would be represented in R: (i) 9.25 (ii) -3.5
- Suppose there are less than 1,000,000,000,000,000,000,000 (or 10) stars in the universe. If you have to store that number (Any integer or round number less than 10) exactly in a floating-point number (Stored in binary), minimum how many bits must be in mantissa and exponent?Problem: You have the table below of values of telemetry from the satellite. The temperatures are encoded linearly in unsigned binary bytes as a function of time. The samples come in every five minutes starting at time = 0. The temperatures are in degC and the temperature of -50 degC corresponds to a telemetry value of 0, while a temperature of 100 degC corresponds to a telemetry value of 255. (All values are decimal unless explicitly stated otherwise.) Write down the equation that describes the temperature as a function of telemetry value in the form of T = a* TV + b. What is the value of a? What is the value of b? After your data has been downlinked, as shown in the table below, fill in the Time and Temperature columns (to one place past the decimal point for the Temperature). Sample Telemetry value Time (minutes) Temperature (degC) 1 2 3 4 5 6 7 8 9 10 11 12 13 10 12 14 17 21 41 81 181 210 220 215 222 225 0 5 10 60 -44.1 -42.9 -41.8 82.3A barcode scanner for Universal Product Codes (UPCs) verifies the 12-digit code scanned by comparing the code's largest digit (called a check digit) to its own computation of the check digit from the first 11 digits as follows: 1. Calculate the sum of the digits in the odd-numbered positions (the first, third,..... eleventh digits) and multiply this sum by 3. 2. Calculate the sum of the digits in the even-numbered position (the second, fourth....tenth digits) and add this to the previous result. 3. If the last digit of the result from step 2 is 0, then 0 is the check digit. Otherwise, subtract the last digit from 10 to calculate the check digit. 4. If the check digit matches the final digit of the 12-digit UPC, the UPC is assumed correct By using C++ write a program that prompts the user to enter the 12 digits of a barcode separated by space. The program should store the digits in an integer array, calculate the check digit, and compare it to the final barcode digit. If the digits…
- 1): The prime factorization of 198 is 198 = 2 · 32 · 11 A): 2 · 3.3· 11 B): 2.33.3 C): 1.198 D): 18.11 2): Some numbers and their prime factorizations are given below. 140 = 22 5 · 7 175 = 52 7 532 = 22 7 · 19 648 = 23 34 1078 = 2 · 72 11 1083 = 3 · 192 15435 = 32 5 · 73 1078 = 2 · 72 11 25480 = 23 5 · 72·13 Using these prime factorizations the gcd(532, 15435) = A): 7 B): 52 C): 97 D): 77 3): Applying the Euclidean Algorithm and the Extended Euclidean Algorithm. the gcd(81,60) , and expression of the gcd as a linear combination of the two numbers = A): gcd=3, combination = 3.81-4.60 B): gcd=3, combination = 21-18 C): gcd=12, combination = 81-69 D): gcd=9, combinaton = 81-60-12 4): using arithmetic in the ring of integers mod 9, 5×8inZ9= A): 4 B): 36 C): 2 D): 03) Represent following floating-point numbers in IEEE single-precision (32- bit) format: a. -0.75, b. 3.0 Show the steps done to reach the answer for each (i.e. how to get the S-bit, the exponent, and the fraction field of the answer).2. Perform the following number system conversions directly without converting them to decimal: (a) 10100.11012 = ?16 (b) 67.23s = ?2 %3D (c) 101111.01112 = ?s (d) 15C.3816 = ?2 %3D
- In this question, you are provided with an IEEE-754 floating-point number in the form of 8 hexadecimal digits. You are asked to decode this value into its decimal representation. Do NOT use scientific notation. Do NOT round or truncate your answer. Do NOT add any spaces or commas to your answer. If the converted number is positive, do NOT add the plus sign. Your answer will consist of two parts, the integer value and the fraction value. Do not add any insignificant zeros to your answer. For the fraction part, you can start it by a decimal point or by a single 0, followed by a decimal point. Convert, i.e., decode, 0x48804008 from the 32-bit single-precision IEEE-754 FP representation into decimal representation. The integer part of the number is: D The fractional part of the number (including the decimal point) is: bAn interesting application of a PLA is conversion from the old, obsolete punched cards character codes to ASCII codes. The standard punched cards that were so pop- ular with computers in the past had 12 rows and 80 columns where holes could be punched. Each column corresponded to one character. so each character had a 12-bit code. However, only 96 characters were actually used. Consider an application that reads punched cards and converts the character codes to ASCII. a. Describe a PLA implementation of this application. b. Can this problem be solved with a ROM? Explain.1) For IEEE 754 single precision floating point numbers, if X is a negative denormalized floating point number with mantisa 010 0000 0000 0000 0000 0000, what is the decimal value of X? Question options: a. –1.25 × 2^(–126 ) b. –1.25 × 2^(–127 ) c. –0.25 × 2^(–127) d. –0.25 × 2^(–126 ) e. None of the above 2) Which of following recursive C++ functions correctly computes a[0]+a[1]+...+a[n-1] (where n is the size of array a) ? Question options: int sum(int n, int a[] ){ return n>0? sum(n-1) + a[n] : a[0]; } int sum(int n, int a[] ){ return n>0? sum(n-1, a) + a[n-1] : a[0]; } int sum(int n, int a[] ){ return sum(n-1, a) + a[n-1] ; } int sum(int n, int a[] ){ return n>0? sum(n-1, a) + a[n] : a[0]; } int sum(int n, int a[] ){ return n>0? sum(n-1) + a[n-1] : a[0]; }
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