Explanation Given: The expression, 10111 two + 11110 two − 111 two . Explanation: Since, the given computation involves base two, the only allowed numbers are 0 and 1. Break the given computation into two parts. First, add 10111 two + 11110 two and then subtract 111 two from the result of the addition. To add two numbers, first write the two numbers one over the other, such that the digits corresponding to the same place value come in one line and then add column by column: 10111 two + 11110 two _ Now, add the two digits in the first column from right: 1 two + 0 two = 1 ten = ( 1 × 1 ) = 1 two . Write 1 two in the first column from right, below the horizontal line: 10111 two + 11110 two _ 1 two Now, add the two digits in the second column from right: 1 two + 1 two = 2 ten = ( 1 × 2 ) + ( 0 × 1 ) = 10 two . Write 0 two in the second column from right, below the horizontal line, and carry 1 two to the third column from right: 10 1 1 11 two + 11110 two _ 01 two Now, add the three digits in the third column from right: 1 two + 1 two + 1 two = 3 ten = ( 1 × 2 ) + ( 1 × 1 ) = 11 two . Write 1 two in the third column from right, below the horizontal line, and carry 1 two to the fourth column from right: 1 0 1 111 two + 11110 two _ 101 two Now, add the two digits in the fourth column from right: 1 two + 1 two = 2 ten = ( 1 × 2 ) + ( 0 × 1 ) = 10 two . Write 0 two in the fourth column from right below the horizontal line, and carry 1 two to the fifth column from right: 1 1 0111 two + 11110 two _ 0101 two Now, add the three digits in the fifth column from right: 1 two + 1 two + 1 two = 3 ten = ( 1 × 2 ) + ( 1 × 1 ) = 11 two . Write 11 two in front of 0101 two below the horizontal line: 10111 two + 11110 two _ 110101 two Now, subtract 111 two from 110101 two

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Author: Blitzer

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Chapter 4.3, Problem 42E

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The simplified answer of the given expression 10111two+11110two−111two.

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Chapter 4.3, Problem 41E

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The simplified answer of the given expression 10111 two + 11110 two − 111 two .

Solution Summary: The author explains how to determine the simplified answer of the given expression, 10111_two+11110

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