Introduction To Computing Systems
3rd Edition
ISBN: 9781260150537
Author: PATT, Yale N., Patel, Sanjay J.
Publisher: Mcgraw-hill,
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Question
Chapter 2, Problem 34E
a.
Program Plan Intro
NOT operation:
- NOT function needs one input and produces one output.
- It is also known as unary logical function.
- Another name of NOT operation is complementary operation.
- Output is produced by complementing the input.
- The following diagram depicts the NOT operation,
- The NOT operation produces the output “1”, when the source input is “0”.
- The NOT operation produces the output “0”, when the source input is “1”.
- The truth table for the NOT operation is as follows,
| X | |
| 0 | 1 |
| 1 | 0 |
- In the above table, “X” is the input, and “Z” is the output.
- When “X=0”, the output “Z” is the complement of “0”, which means “1” and When “X=1”,the output “Z” is the complement of “1”, which means “0”.
OR operation:
- OR function needs two inputs and produces one output.
- It is also known as binary logical function.
- If one of the inputs or both the inputs are “1”, then one-bit OR operation produces the output as “1”.
- If both the inputs are “0”, then OR operation produces the output “0”.
- The following diagram depicts the one-bit OR operation,
- The truth table for OR operation is as follows,
| X | Y | Z=X OR Y |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
- In the above table, “X” and “Y” are the inputs, and “Z” is the output.
- In the above table, when “X=0”, and “Y=0”, the output “Z” is “0”, because both the inputs “X” and “Y” contains the value “0”.
- When “X=0”, and “Y=1”, the output “Z” is “1”, because one of the input “Y” contains the value “1”.
- When “X=1”, and “Y=0”, the output “Z” is “1”, because one of the input “X” contains the value “1”.
- When “X=1”, and “Y=1”, the output “Z” is “1”, because both the inputs “X” and “Y” contains the value “1”.
AND function:
- AND function needs two inputs and produces one output.
- It is also known as binary logical function.
- If one or both the inputs are “0”, then one-bit AND operation produces the output “0”.
- If both inputs are “1”, then AND operation produces the output as “1”.
- The following diagram depicts the AND operation,
- The truth table for AND operation is as follows,
| X | Y | X AND Y |
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
- In the above table, “X” and “Y” are inputs, and “Z” is output.
- When “X=0”, and “Y=0”, the output is “0”, because both the inputs “X” and “Y” contains the value “0”.
- When “X=0”, and “Y=1”, the output is “0”, because one of the input “X” contains the value “0”.
- When “X=1”, and “Y=0”, the output is “0”, because one of the input “Y” contains the value “0”.
- When “X=1”, and “Y=1”, the output is “1”, because both the inputs “X” and “Y” contains the value “1”.
b.
Explanation of Solution
To compute “NOT (1000 AND (1100 OR 0101))”:
- To compute “(1100 OR 0101)”,
- The OR operation can be applied on each pair of bits individually and hence it is called bit-wise OR operation.
- The OR operation for the binary numbers “1100” and “0101” is as follows,
- The output bit is “1”, when one or both of the input bits are “1” and the output bit is “0”, when both the input bits are “0”.
- The result of “(1100 OR 0101)” is “1101”.
- To compute “1000 AND (1100 OR 0101))”,
- Compute the AND operation for the binary number “1000” and the result “1101”.
- The AND operation can be applied on each pair of bits individually and hence it is called bit-wise AND operation.
- The AND operation for the given binary number is as follows,
c.
Explanation of Solution
To compute “NOT(NOT(1101))”:
- First compute “NOT (1101)”,
- The NOT operation can be applied on each bits individually and hence it is called bit-wise NOT operation.
- The NOT operation for the binary number “1101” is as follows,
- The output bit is “0”, when the input bit is “1” and the output bit is “1”, when the input bit is “0”.
- The result of the above calculation is “0010”...
d.
Explanation of Solution
To compute “(0110 OR 0000) AND 1111”:
- First compute “(0110 OR 0000)”,
- The OR operation can be applied on each pair of bits individually and hence it is called bit-wise OR operation.
- The OR operation for the given binary number is as follows,
- The output bit is “1”, when one or both of the input bits are “1” and the output bit is “0”, when both the input bits are “0”.
- The result of the above calculation is “0110”.
- Compute “0110 AND 1111”,
- The AND operation can be applied on each pair of bits individually and hence it is called bit-wise AND operation...
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Chapter 2 Solutions
Introduction To Computing Systems
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