Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 4 - Number Representation and Calculation - 4.3 Computation in Positional Systems - Exercise Set 4.3 - Page 235: 49

Answer

The output of the AND gate will be 10001, and output of the OR gate will be 11001.

Work Step by Step

The AND gate takes two inputs and produces one output. It outputs 1 only when both the inputs are 1, otherwise, it outputs 0. In the given question, the binary sequences 10011 and 11001 are being fed to the AND gate as inputs. Write both the inputs one over the other: 10011 11001 Now, find the output of AND gate for the above two inputs column by column, starting from rightmost column: 1 and 1 will give 1. 1 and 0 will give 0. 0 and 0 will give 0. 0 and 1 will give 0. 1 and 1 will give 1. Hence, the output of AND gate will be 10001. Now, the output of AND gate, 10001, and the binary sequence 11001 are being fed to the ORgate as inputs. Write both the inputs one over the other: 10001 11001 The OR gate takes two inputs and produces one output. It outputs 1 as long as at least one of the inputs is 1. If both the inputs are 0, it outputs 0. Now, find the output of OR gate for the above two inputs column by column, starting from rightmost column: 1 and 1 will give 1. 0 and 0 will give 0. 0 and 0 will give 0. 0 and 1 will give 1. 1 and 1 will give 1. Hence, the output of OR gate will be 11001. And, the final outputs of all the gates in the given figure can be shown as:
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