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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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?
Is there a way to efficiently employ decimal data types, and what are
the benefits and drawbacks of doing so?
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
- Using MIPS in assembly language, you are 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. *Also have a lot of comments in your program as this is an assembly language program. Make the code neat and readable.arrow_forwardWrite 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 1011100100010000000000000000000000000000000000000000arrow_forwardFind three floating-point values to illustrate that floatingpointaddition is not associative?arrow_forward
- Consider 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_forwardYou 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_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
- A video frame displayed onscreen consists of many pixels, with eachpixel, or cell, representing one unit of video output. A videodisplay’s resolution is typically specified in horizontal and verticalpixels (such as 1920 3 1080), and the number of pixels onscreen issimply the product of these numbers (1920 3 1080 5 2,073,600 pixels).A pixel’s data content is one or more unsigned integers. For ablack-and-white display, each pixel is a single number (usuallybetween 0 and 255) representing the intensity of the color white.Color pixel data is typically represented as one or three unsignedintegers.When three numbers are used, the numbers are usually between 0 and255, and each number represents the inten- sity of a primary color(red, green, or blue). When a single number is used, it represents apredefined color selected from a table (palette) of colors.Motion video is displayed onscreen by copying frames rapidly to thevideo display controller. Because video images or frames require manybytes…arrow_forwardAs calculating floating-point arithmetic is done by a digital computers,there is often some mistake, as in all complex numbers have an inherent irrational component.explain?arrow_forwardOne way to electrically or optically represent a binary 1 or 0 is to use the transition between a voltage level (for example, going from a state of no voltage to a state of voltage, or vice versa, on a copper cable) or the transition of having light or no light on a fiber-optic cable to represent a binary 1. Similarly, a binary 0 is represented by having no transition in a voltage level or light level from one time period to the next. This approach of representing binary digits is called state transition modulation.arrow_forward
- If you have access to the natural log function ln(x), specify how you could use it to implement a log(b, x) function where b is the base of the log. What should the function do for negative b values? Assume an IEEE floating point implementation.arrow_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_forwardThe IEEE Standard 754 representation of a floating point numberis given as: 01101110110011010100000000000000. Determine thebinary value represented by this number. If a computer’s system clock is 2.4 GHz, calculate the period of thesystem clock. If an 8-bit binary number is used to represent an analog value inthe range from 200 ounces to 700 ounces, what is the resolution ofthe system?arrow_forward
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