
Concept explainers
Convert the following base-2 numbers to base-10: (a) 101101, (b) 101.011, and (c) 0.01101.
(a)

To calculate: The number in base-10 if the number in base-2 is
Answer to Problem 1P
Solution:
The number in base-10 is
Explanation of Solution
Given:
The number in base-2 is
Formula used:
Conversion formula from base-2 to base-10,
Where, N is real positive number, b is the digit and I is the integer.
Calculation:
Consider the Base-2 Number,
Convert this number to Base-10 number by multiplying the place values to the digits and adding them together.
The place value of the digits are
Therefore,
Hence, the converted base-10 value of the base-2 number is
(b)

To calculate: The number in base-10 if the number in base-2 is
Answer to Problem 1P
Solution:
The number in base-10 is
Explanation of Solution
Given:
The number in base-2 is
Formula used:
Conversion formula from base-2 to base-10,
Where, N is real positive number, b is the digit and I is the integer.
Calculation:
Consider the Base-2 Number,
Convert this number to Base-10 number by multiplying the place values to the digits and adding them together.
In this case the binary digits after the point has place values
Hence, the converted base-10 value of the base-2 number is
(c)

To calculate: The number in base-10 if the number in base-2 is
Answer to Problem 1P
Solution:
The number in base-10 is
Explanation of Solution
Given:
The number in base-2 is
Formula used:
Conversion formula from base-2 to base-10,
Where, N is real positive number, b is the digit and I is the integer.
Calculation:
Consider the Base-2 Number,
In this case the binary digits after the point has place values
Hence, the converted base-10 value of the base-2 number is
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Chapter 3 Solutions
Numerical Methods for Engineers
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