Concept explainers
Videos
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 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)
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 2−1, 2−2, 2−3 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+0×2−1+1×2−2+1×2−3=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)
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 2−1, 2−2, 2−3, 2−4, 2−5, 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+0×2−1+1×2−2+1×2−3+0×2−4+1×2−5=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.
Want to see more full solutions like this?
Chapter 3 Solutions
Numerical Methods for Engineers
- Problems Construct shear and moment diagrams using the equilib- rium method. Indicate the magnitudes of Vmax and Mmax. 7.3 107 B 5' 201arrow_forwardCan you help me with this problem using linear recurrance: Find an explicit formula for the recurrence relation an = 2can−1 + 3c2an−2 where c not equal to 0 with initial conditions a0=4c and a1 = 0arrow_forwardCan you help me solved this problem using generalized combination:How many combinations are there to pick r objects from 2n objects numbered from 1to 2n when repetitions are allowed and at least one object of odd type does not appear?arrow_forward
- In Exercises 1-14, state whether each statement is true or false. If false, give a reason. 1. The set of stores located in the state of Wyoming is a well- defined set. 2. The set of the three best songs is a well-defined set. 3. maple = {oak, elm, maple, sycamore} 4{} cơ 5. {3, 6, 9, 12,...} and {2, 4, 6, 8, ...} are disjoint sets. 6. {Mercury, Venus, Earth, Mars} is an example of a set in roster form. 7. {candle, picture, lamp} = {picture, chair, lamp } 8. {apple, orange, banana, pear} is equivalent to {tomato, corn, spinach, radish}.arrow_forwardExercises Evaluate the following limits. 1. lim cot x/ln x +01x 2. lim x² In x +014 3. lim x* x0+ 4. lim (cos√√x)1/x +014 5. lim x2/(1-cos x) x10 6. lim e*/* 818 7. lim (secx - tan x) x-x/2- 8. lim [1+(3/x)]* x→∞0arrow_forwardIn Exercises 1 through 3, let xo = O and calculate P7(x) and R7(x). 1. f(x)=sin x, x in R. 2. f(x) = cos x, x in R. 3. f(x) = In(1+x), x≥0. 4. In Exercises 1, 2, and 3, for |x| 1, calculate a value of n such that P(x) approximates f(x) to within 10-6. 5. Let (an)neN be a sequence of positive real numbers such that L = lim (an+1/an) exists in R. If L < 1, show that an → 0. [Hint: Let 1111 Larrow_forward
- iation 7. Let f be continuous on [a, b] and differentiable on (a, b). If lim f'(x) xia exists in R, show that f is differentiable at a and f'(a) = lim f'(x). A similar result holds for b. x-a 8. In reference to Corollary 5.4, give an example of a uniformly continuous function on [0, 1] that is differentiable on (0, 1] but whose derivative is not bounded there. 9. Recall that a fixed point of a function f is a point c such that f(c) = c. (a) Show that if f is differentiable on R and f'(x)| x if x 1 and hence In(1+x) 0. 12. For 0 л/2. (Thus, as x л/2 from the left, cos x is never large enough for x+cosx to be greater than л/2 and cot x is never small enough for x + cot x to be less than x/2.)arrow_forward1. Show that f(x) = x3 is not uniformly continuous on R. 2. Show that f(x) = 1/(x-2) is not uniformly continuous on (2,00). 3. Show that f(x)=sin(1/x) is not uniformly continuous on (0,л/2]. 4. Show that f(x) = mx + b is uniformly continuous on R. 5. Show that f(x) = 1/x2 is uniformly continuous on [1, 00), but not on (0, 1]. 6. Show that if f is uniformly continuous on [a, b] and uniformly continuous on D (where D is either [b, c] or [b, 00)), then f is uniformly continuous on [a, b]U D. 7. Show that f(x)=√x is uniformly continuous on [1, 00). Use Exercise 6 to conclude that f is uniformly continuous on [0, ∞). 8. Show that if D is bounded and f is uniformly continuous on D, then fis bounded on D. 9. Let f and g be uniformly continuous on D. Show that f+g is uniformly continuous on D. Show, by example, that fg need not be uniformly con- tinuous on D. 10. Complete the proof of Theorem 4.7. 11. Give an example of a continuous function on Q that cannot be continuously extended to R. 12.…arrow_forwardcan I see the steps for how you got the same answers already provided for μ1->μ4. this is a homework that provide you answers for question after attempting it three triesarrow_forward
Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL