Programmable Logic Controllers
5th Edition
ISBN: 9780073373843
Author: Frank D. Petruzella
Publisher: McGraw-Hill Education
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Chapter 3, Problem 9P
Explanation of Solution
Using a floating-point numbering system:
- Sometimes it is necessary to adjust the decimal point of a binary number, especially when computing arithmetic and logic operations.
- This representation is useful to increase or decrease the significant value.
- Floating point binary representation can also be used to represent negative numbers by simple binary format...
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Students have asked these similar questions
The assignment is to create a MIPS program that demonstrates that the associative law fails in addition for floating point numbers (single or double precision). You only need to demonstrate it for single precision. Remember the associative law is a + (b + c) = (a + b) + c.
The key is to have two of the number large (one positively and one negatively but equal in magnitude) floating point numbers and the third floating point number very small in comparison.
***Please make sure you include comments in every field***
Note: make sure the program operats and doesnt run with errors like: operand is of incorrect type or not formatted
Scenario: 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?
Write down the mathematical notation for fixed point representationand floating representation and also explain each term.
Consider the following machine number in 64 bit and Precisely represent the above machine number in decimal digits.
0 10000000011 1011100100010000000000000000000000000000000000000000
Chapter 3 Solutions
Programmable Logic Controllers
Ch. 3 - Prob. 1RQCh. 3 - Convert each of the following decimal numbers to...Ch. 3 - Prob. 3RQCh. 3 - Prob. 4RQCh. 3 - Prob. 5RQCh. 3 - Prob. 6RQCh. 3 - Prob. 7RQCh. 3 - Prob. 8RQCh. 3 - Prob. 9RQCh. 3 - Prob. 10RQ
Ch. 3 - Prob. 11RQCh. 3 - Define the term sign bit.Ch. 3 - Prob. 13RQCh. 3 - Prob. 14RQCh. 3 - Prob. 15RQCh. 3 - Prob. 16RQCh. 3 - Prob. 17RQCh. 3 - Prob. 18RQCh. 3 - Prob. 19RQCh. 3 - Prob. 1PCh. 3 - Prob. 2PCh. 3 - Prob. 3PCh. 3 - Prob. 4PCh. 3 - Prob. 5PCh. 3 - Prob. 6PCh. 3 - Prob. 7PCh. 3 - Prob. 8PCh. 3 - Prob. 9PCh. 3 - Prob. 10P
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Similar questions
- You have to design a processing unit dealing with floating point numbers. The main purpose of using floating point numbers in your case is to make comparisons between two floating point numbers (a and b) in order to know if they are equal or not. If not, to know if a is strictly greater or smaller than b. For the mantissa and exponent, which represention you may choose or not and why, having in mind to have the fastest comparison operator as possible? Describe the algorithm you may use to do the comparison?arrow_forwardConsider a 32-bit number stored in a byte-addressable memory as shown in the table below (note that the value is written in hex format): a. If the machine is little endian and uses 2's complement representation for integers, give the decimal representation of the 32-bit integer that starts at address 100. b. If the machine is big endian and the number is an IEEE single precision floating point value, give the decimal equivalent. Note the following: • When converting the binary significand to its base 10 equivalent, you only need to use the first 8 bits (not all 23) The final answer should be written as a simple real number (i.e., not in exponential format), with the fractional component rounded to 2 decimal places (e.g., 126.46 or -9768.83) Value Address 100 101 102 103 40 92 9C FBarrow_forwardConsider a new floating point representation, which we will call here the CMPT215Float16 representation. The CMPT215Float16 representation follows the IEEE 754 binary floating point standard, but with smaller-sized fields for the exponent and fraction. In particular, CMPT215Float16 numbers have a 1-bit sign field, followed by a 7-bit exponent field (in biased notation, with a bias of only 63 because of the smaller size of this field), followed by an 8-bit fraction field. Give, in decimal, the quantity represented by the following CMPT215Float16 floating point value: 0100001110100000.arrow_forward
- What is -1011.1 in floating point representationarrow_forwardThis is an VERILOG HDL topic. I need help on this review question. Please explain well so that I could understand.arrow_forwardYou are asked to design a system of FP numbers representation (with your own design choices), labeled Custom_FP_48, for which we have 48 bits at our disposal in order to represent a number, in analogy with the IEEE 754 prototype. You are asked to provide: a) The types for evaluating this number b) The width of representation of these numbers (upper and lower) c) The maximum precision (i.e., the minimum difference between two successive numbers).arrow_forward
- 2. Say you're working in a floating point system with base () of 2, precision (p) of 3 and allowable exponents (e) from -1 to 1, as we discussed in class. There are only 25 numbers you can represent in this system. What are they? Remember that every number in a floating point system can be represented as +...+ Where d, =1 and d;=the i digit out of p-1 digits that the computer uses to store the number.arrow_forwardGive (in decimal) the quantity represented by each of the following IEEE 754 single precision floating point values. (a)10111111100000000000000000000000 (b)00000000000000000000000000000000 (c)01111111111111111111111111111111 (d)11000001110110000000000000000000arrow_forwardConsider a 16-bit binary floating point number representation system: + | SE E E E E E m m т m m m m m m The first bit of the exponent is dedicated to its sign. Assume that the mantissa must start with a '1'. Use this system to answer the following question What is the smallest (magnitude) number that can be represented with this system?arrow_forward
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