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88-89. Binary numbers Humans use the ten digits 0 through 9 to form base-10 or decimal numbers, whereas computers calculate and store numbers internally as binary numbers–numbers consisting entirely of O's and l's. For this exercise, we consider binary numbers that have the form 0.b,b,b, ..., where each of the digits b,, b,, b, . . . is either 0 or 1. The base-10 representation of the binary number 0.b,b,b, ... is the b, b3 b, 2! 22 infinite series Computers can store only a finite number of digits and therefore numbers with nonterminating digits must be rounded or truncated before they can be used and stored by a computer. a. Find the base-10 representation of the binary number 0.0011. b. Suppose a computer rounds the binary number 0.0011 to b = 0.0011001100110011 before storing it. Find the approxi- mate base-10 representation of b, rounding your answer to 8 digits to the right of the decimal place.

88-89. Binary numbers Humans use the ten digits 0 through 9 to form base-10 or decimal numbers, whereas computers calculate and store numbers internally as binary numbers–numbers consisting entirely of O's and l's. For this exercise, we consider binary numbers that have the form 0.b,b,b, ..., where each of the digits b,, b,, b, . . . is either 0 or 1. The base-10 representation of the binary number 0.b,b,b, ... is the b, b3 b, 2! 22 infinite series Computers can store only a finite number of digits and therefore numbers with nonterminating digits must be rounded or truncated before they can be used and stored by a computer. a. Find the base-10 representation of the binary number 0.0011. b. Suppose a computer rounds the binary number 0.0011 to b = 0.0011001100110011 before storing it. Find the approxi- mate base-10 representation of b, rounding your answer to 8 digits to the right of the decimal place.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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88-89. Binary numbers Humans use the ten digits 0 through 9 to form base-10 or decimal numbers, whereas computers calculate and store numbers internally as binary numbers–numbers consisting entirely of O's and l's. For this exercise, we consider binary numbers that have the form 0.b,b,b, ..., where each of the digits b,, b,, b, . . . is either 0 or 1. The base-10 representation of the binary number 0.b,b,b, ... is the b, b3 b, 2! 22 infinite series Computers can store only a finite number of digits and therefore numbers with nonterminating digits must be rounded or truncated before they can be used and stored by a computer. a. Find the base-10 representation of the binary number 0.0011. b. Suppose a computer rounds the binary number 0.0011 to b = 0.0011001100110011 before storing it. Find the approxi- mate base-10 representation of b, rounding your answer to 8 digits to the right of the decimal place.
Transcribed Image Text:88-89. Binary numbers Humans use the ten digits 0 through 9 to form base-10 or decimal numbers, whereas computers calculate and store numbers internally as binary numbers–numbers consisting entirely of O's and l's. For this exercise, we consider binary numbers that have the form 0.b,b,b, ..., where each of the digits b,, b,, b, . . . is either 0 or 1. The base-10 representation of the binary number 0.b,b,b, ... is the b, b3 b, 2! 22 infinite series Computers can store only a finite number of digits and therefore numbers with nonterminating digits must be rounded or truncated before they can be used and stored by a computer. a. Find the base-10 representation of the binary number 0.0011. b. Suppose a computer rounds the binary number 0.0011 to b = 0.0011001100110011 before storing it. Find the approxi- mate base-10 representation of b, rounding your answer to 8 digits to the right of the decimal place.
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