1. Two's complement notation really shows its value in binary addition, where positive and negative quantities may be handled with equal ease. Add the following byte-long (8 bit) two's complement numbers together, and then convert all binary quantities into decimal form to verify the accuracy of the addition: (show Work) a. 00110101 +00001100 00001010 +10010101 01110110 +00000010 11111110 +11011101 00111101 +11111011 11111110 +11111101

1. Two's complement notation really shows its value in binary addition, where positive and negative quantities may be handled with equal ease. Add the following byte-long (8 bit) two's complement numbers together, and then convert all binary quantities into decimal form to verify the accuracy of the addition: (show Work) a. 00110101 +00001100 00001010 +10010101 01110110 +00000010 11111110 +11011101 00111101 +11111011 11111110 +11111101

Systems Architecture

7th Edition

ISBN:9781305080195

Author:Stephen D. Burd

Publisher:Stephen D. Burd

Chapter3: Data Representation

Section: Chapter Questions

Problem 4PE

See similar textbooks

Similar questions

___________ occurs when the result of an arithmetic operation exceeds the number of bits available to store it.
8. 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. 1111 0010 + 1101 0110 ----------- Overflow? Yes or No Carry? Yes or No
6. Convert the following numbers from unsigned binary notation to decimal notation, and from 6-bit 2's complement notation to decimal notation: i) 110011, ii) 001101, iii) 101101 7. Show how each of the following floating point values would be stored using IEEE-754 single precision (be sure to indicate the sign bit, the exponent, and the significand fields): a. 12.5 b. −1.5 c. 0.75 d. 26.625 8. The following is a representation of a decimal floating value using IEEE-754 single precision. Find out the value in decimal. 0 10000011 10101000000...0
Show Steps Please 18. If the floating-point number representation on a certain system has a sign bit, a 3-bit exponent and a 4-bit significand: a) What is the largest positive and the smallest positive number that can be stored on this?system if the storage is normalized? (Assume no bits are implied, there is no biasing, exponents use two's complement notation, and exponents of all zeros and all ones are allowed.) b) What bias should be used in the exponent if we prefer all exponents to be non-negative? c) Why would you choose this bias?
Calculate (3.41700875 *10-3 + 6.34005625*10-3)* 1.25625* 102 by hand, assuming each of the values are stored in the 16-bit half precision format describedin in the textbook. Assume 1 guard, 1 round bit, and 1 sticky bit, and round to thenearest even. Show all the steps, and write your answer in both the 16-bit floating point format and in decimal.
Show Steps Please 21. Suppose we want an error-correcting code that will allow all single-bit errors to be corrected for memory words of length 10. a) How many parity bits are necessary? b) Assuming we are using the Hamming algorithm presented in this chapter to design our error-correcting code, find the code word to represent the 10-bit information word: 1001100110. 22. Using the CRC polynomial 1101, compute the CRC code word for the information word, 01001101. Check the division performed at the receiver.
Negative signed binary numbers What is the decimal representation of the 2-bit signed binary number 11? What is the decimal representation of the 16-bit signed binary number 1111_1111_1111_1111? How do the signed binary representations differ (ignoring the underscores)? What is the decimal representation of the 8-bit signed binary number 1001_0001? What is the decimal representation of the 16-bit signed binary number 1111_1111_1001_0001? How do the signed binary representations differ (ignoring the underscores)? What is the decimal representation of the 9-bit signed binary number 1_0001_0001? What is the decimal representation of the 16-bit signed binary number 1111_1111_0001_0001?
Explain the term masking. How is it useful for data representation? Explain the concept using an example For a floating-point format with a k -bit exponent and an n -bit fraction, give a formula for the smallest positive integer that cannot be represented exactly (because it would require an n + 1 –bit fraction to be exact).
a) A digital sound recorder captures sound from the real-world, processes the audio and stores it in binary form. Using the principles of digital signal processing, practically explain how this phenomenon occurs. b) Use the two’s complement binary representation to represent each of the following integers as 10-bit binary numbers.i) -13710 ii) 14510 iii) -15810 iv) 16710 v) -11510 c) If an 8-bit binary number is used to represent an analog value in the range from 0 to 100kg, what does the binary value 011001002 represent?
Given the following decimal numbers, convert the numbers to a 16-bit memory location in binary using two's complement. (show all details step by step) 165910 - 165910 954610 - 954610 Convert the following decimal numbers to binary using the two’s complement format, using 8 bits: 4810 -3910 -28410 010 Briefly explain why two’s complement is the best format for representing signed integers in a computer. 4. Convert the following decimal numbers to binary floating-point representation, using 4 bits for the fractional part: 68.510 125.4410 99.9910 give the answer of everything otherwise dont give. please
The following is a string of ASCII characters whose bit patterns have been converted intohexadecimal for compactness: 73 F4 E5 76 E5 4A EF 62 73. Of the eight bits in each pairof digits, the leftmost is a parity bit. The remaining bits are the ASCII code.(a) Convert the string to bit form and decode the ASCII.(b) Determine the parity used: odd or even?
Assume we have a byte system for the fixed number representation (the whole number is presented with 8-bits (one byte) and the fractional part is presented with 2-bits), find the 2's complement of 0110 0010.01 The answer should be formatted as a fractional 2's complement binary number representation with the exact format of the answer that is required of this particular calculation. I've gotten an answer of 1001 1110.00 but it says its wrong please help