Numerical Methods for Engineers
Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Chapter 3, Problem 1P

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

(a)

Expert Solution
Check Mark
To determine

To calculate: The number in base-10 if the number in base-2 is 101101.

Answer to Problem 1P

Solution:

The number in base-10 is 45.

Explanation of Solution

Given:

The number in base-2 is 101101.

Formula used:

Conversion formula from base-2 to base-10,

N=ibi2i

Where, N is real positive number, b is the digit and I is the integer.

Calculation:

Consider the Base-2 Number, 101101 .

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 2+5, 2+4, 2+3, 2+2, 2+1, 20 from left to right.

Therefore,

(101101)2=1×2+5+0×2+4+1×2+3+1×2+2+0×2+1+1×20=32+0+8+4+0+1=(45)10

Hence, the converted base-10 value of the base-2 number is 45 .

(b)

Expert Solution
Check Mark
To determine

To calculate: The number in base-10 if the number in base-2 is 101.011.

Answer to Problem 1P

Solution:

The number in base-10 is 5.375.

Explanation of Solution

Given:

The number in base-2 is 101.011.

Formula used:

Conversion formula from base-2 to base-10,

N=ibi2i

Where, N is real positive number, b is the digit and I is the integer.

Calculation:

Consider the Base-2 Number, 101.011 .

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 21, 22, 23 from left to right and 2+2, 2+1, 20 from left to right before the point. Therefore,

(101.011)2=1×2+2+0×2+1+1×20+0×21+1×22+1×23=4+0+1+0+0.25+0.125=(5.375)10

Hence, the converted base-10 value of the base-2 number is 5.375 .

(c)

Expert Solution
Check Mark
To determine

To calculate: The number in base-10 if the number in base-2 is 0.01101.

Answer to Problem 1P

Solution:

The number in base-10 is 0.40625.

Explanation of Solution

Given:

The number in base-2 is 0.01101.

Formula used:

Conversion formula from base-2 to base-10,

N=ibi2i

Where, N is real positive number, b is the digit and I is the integer.

Calculation:

Consider the Base-2 Number, 0.01101 .

In this case the binary digits after the point has place values 21, 22, 23, 24, 25, from left to right. So, multiply the place values with the digits of the base-2 number and add them to get the base-10 number.

(0.01101)2=0×20+0×21+1×22+1×23+0×24+1×25=0+0+0.25+0.125+0+0.03125=(0.40625)10

Hence, the converted base-10 value of the base-2 number is 0.40625.

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