3.6: Radom Number and Logical Operators
- Page ID
- 126553
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Random Number Function
In C++, the function rand() produces a random number between 0 and 32,767. If we want to get a random number between 0 and 9, we use rand()%10. Similarly, if we want to get a random number between 0 and 99, we use rand()%100. In general, the code rand()%n in a C++ program will generate a random number between 0 and n-1.
If you would like to random get a number between 1 and 10, you can use the code
rand()%10 + 1
If you want to random generate a number between 65 and 90, you can use the code
rand()%26+65
We will use a random number function in a C++ program discussed in Section 3.8: Case Study: Practice Multiplication
Logical Operators
Sometimes, in the C++ programming, we need to use relational statements that are formed by connecting two or more simple relational statements. The symbols or the words we use in C++ programming for connecting relational statements are called logical operators. The commonly used logical operators are
- or, this is also called a union operator. Alternatively, it can also be codded as || (two vertical bars with no space in between)
- and, this is also called an intersection operator. Alternatively, it can also be codded as && (shift key + 7, two of those with no space in between)
- not, this is also called a negation operator. Alternative, it can also be codded as ! (an exclamation mark)
In a C++ program, we use those logical operators to connect one or more simple relational statements to form complex relational statements.
Examples
- (x > 5) or (x < -2)
This is a relational statement formed by connecting two simple relational statements (x>5) and (x<-2) using connectives or. The truth value of this compound relational statement depends on the value of the variable x. If x is a number that is either greater than 5 or less than -2, then the relational statement is true. Otherwise, it is false. In general, if two relational statements are connected with the logical operator 'or', then the compound relational statement is true as long as one of the two relational statements is true, and the compound relational statement is false only when both relational statements are false. - ! (5==7)
This is a relational statement formed by using the negation operator, which is true. Since 5==7 is false and the negation operator '!" negates the Boolean value of 5==7 (the word "negate" means switching the truth value of a relational statement) - ! (a==5)
This is also a relational statement formed by using the negation operator. The truth value of this relational statement depends on the value of the variable a. It is true if the value of the variable a is 5 and it will be false when the variable a actually equals 5. - (a>=200) and (a<=800)
This is a relational statement formed by using the connective and connecting two simple relational statements (a>=200) and (a<=800). The truth value of this compound relational statement depends on the value of the variable a. If the value of the variable a falls between 200 and 800 with 200 and 800 included, then it is true. Otherwise, it is false. In general, if two relational statements are connected with the logical operator 'and', then the compound relational statement is false as long as one of the two relational statements is false, and the compound relational statement is true only when both relational statements are true.