Introduction to Expressions
Types of Values
An expression is a combination of values and symbols used to produce a new value. There are different types of values involved in an expression. They are:
A string is a character, a word, or group of words considered as an entity. Any combination of letters or words you can think is primarily a string.
A Boolean value is one that can be expressed in only one of two values, as either TRUE or as FALSE. A FALSE value also has the value of 0. In this case, any other numeric value is considered TRUE. Boolean values are mostly used in comparisons.
An integer is a natural number that displays without a decimal place. Examples of integers are 18, 16763, and 1450. If the number is very large, it can be considered as a Long integer.
A byte is a small integer that ranges from 0 to 255.
A double, also called double precision, value is a number that can display a decimal portion, using the character set as the decimal separator in Control Panel. For US English, that character would be the period. The expression "double-precision" means that this number provides a high level of precision. If you are dealing with a decimal number but precision is not important, then the number can be represented as a Single. Valid decimal numbers are 12.55, 3.14159 or 9.80336.
A date is a numeric value that counts the number of days that have elapsed from a certain point of reference. How a date displays in a field is based on some conventions set by Microsoft Excel, Microsoft Windows, or you. There are also rules you must respect. Examples of dates are 28/06/1998, 10-8-82, January 10, 1865.
A time is a numeric value that counts the number of seconds that have elapsed since midnight of a certain day. The time also displays following some conventions set in Control Panel, by Microsoft Excel, or the person who created the spreadsheet. Examples of time values are 10:42 AM and 18:06.
The currency is a numeric value used to represent money. In some cases, you can use a double-precision value in place of the currency but because Microsoft Excel is equipped for accounting, you can safely take advantage of the currency type. When using currency rightly, its number presents the character specified in Control Panel. For US English, such a character is $.
A constant is a value that does not change. The constants you will be using in your expressions have already been created and are built-in Microsoft Excel. Normally, Visual Basic for Applications (VBA), the version of Microsoft Visual Basic that ships with Microsoft Excel also provides many constants. Just in case you are aware of them, you will not be able to use those constants, as Microsoft Excel does not inherently “understand” them. For this reason, we will mention here only the constants you can use when building regular expressions.
The algebraic numbers you have been using all the time are constants because they never change. Examples of constant numbers are 12, 0, 1505, or 88146. Therefore, any number you can think of is a constant. Every letter of the alphabet is a constant and is always the same. Examples of constant letters are d, n, c. Some characters on your keyboard represent symbols that are neither letters nor digits. These are constants too. Examples are &, |, @, or !
In Boolean algebra, something is considered True when it holds a value. The value is also considered as 1 or Yes. By contrast, any other value is considered False, 0, or No.
When a field holds a value, the value would be considered using the comparison operators we will learn.
The values we have used so far were provided in cells of a spreadsheet. In some cases, you will need to display a value that is a combination of other values. For example, you may need to combine a first name to a last name to create a full name. In another case, to calculate an employee’s weekly salary, you may need to use the value of a salary and multiply it with a number of hours worked in a week. Most, if not all, of these expressions use what we call operators and operand.
An operation is a technique of using a value or the contents of a cell, or to combine two or more values or contents of cells to either modify an existing value or to produce a new value. Based on this, to perform an operation, you need at least one value or the contents of one cell and one symbol. A value involved in an operation is called an operand. A symbol involved in an operation is called an operator.
When using a worksheet, an expression is entered in a cell and we will see various types of expressions. As done with the other values we have used so far, to create an expression, you first click a cell. If you know the expression you want to use, you can type it either in the cell or in the Formula Bar. In most cases, after typing the expression, you can press Enter (or Tab). In some other cases, as we will see, you can click another cell whose value will complete the expression.
To create an expression, you will use some constants values such as numbers or strings, the operators we are going to study, the names of cells, the names of groups of cells, and sometimes the functions:
After creating the expression, the value of the cell would represented the expression. When you click it, the Formula Bar would display the expression. Here is an example:
In order to display a value in a cell, it must be preceded with the assignment operator, which is “=”. The syntax you would use is:
The operand on the right side of the assignment operator is referred to as the right value or
RValue. It can be a known value or a reference to another cell.
A unary operator is one that uses only one operand. An operator is referred to as binary if it operates on two operands.
The Positive Unary Operator +
Algebra uses a type of ruler to classify numbers. This fictitious ruler has a middle position of zero. The numbers on the left side of the 0 are considered negative while the numbers on the right side of the 0 constant are considered positive:
A value on the right side of 0 is considered positive. To express that a number is positive, you can write a + sign to its left. Examples are +4, +228, and +90335. In this case the + symbol is called a unary operator because it acts on only one operand. The positive unary operator, when used, must be positioned to the left side of its operand.
As a mathematical convention, when a value is positive, you don’t need to express it with the + operator. Just writing the number without any symbol signifies that the number is positive. Therefore, the numbers +4, +228, and +90335 can be, and are better, expressed as 4, 228, or 90335. Because the value does not display a sign, it is referred as unsigned.
The Negative Unary Operator -
In order to express any number on the left side of 0, it must be appended with a sign, namely the - symbol. Examples are -12, -448, and -32706. A value accompanied by - is referred to as negative. The - sign must be typed on the left side of the number it is used to negate.
Remember that if a number doesn’t have a sign, it is considered positive. Therefore, whenever a number is negative, it must have a - sign. In the same way, if you want to change a value from positive to negative, you can just add a - sign to its left. In the same way, if you want to negate the value of a cell, an expression, or a function, you can type the – operator on its left.
Double-quotes are used to enclose a string. As we reviewed earlier, a string can be an empty space, one character, or a group of characters. Such a string must be considered “as is”. Therefore, to include a string in an expression, put it in double-quotes. Examples are “ “, "@", "Hermano", or "Rancho Cordova ".
The & operator is used to append two strings, the contents of two cells, or expressions. This is considered as concatenating them. For example, it could allow you to concatenate a first name and a last name, producing a full name. The general syntax of the concatenation operator is expressed as:
Value1 & Value2
To display a concatenated expression, use the assignment operator on the left of the string. For example, imagine you want to concatenate Juan to Marcus and display the resulting string in cell C5. In C5, you would type =”Juan” & “Markus” and press Enter. The result would be JuanMarkus.
To concatenate more than two expressions, you can use as many & operators between any two expressions as necessary. For example, to add an empty space in the above string, in cell C5, you would type =”Juan” & “ “ & “Markus”
In the same way, you can concatenate the contents of various cells.
The addition is used to add one value or expression to another. It is performed using the + symbol and its syntax is:
Value1 + Value2
The addition allows you to add two numbers such as 12 + 548 or 5004.25 + 7.63
After performing the addition, you get a result. You can display such a result in a cell or use it as an intermediary variable in an expression. For example, to add 242.48 to 95.05 and display the result in cell C6, in C6, you would type =242.48 + 95.05 and press Enter.
The subtraction is performed by retrieving one value from another value. This is done using the - symbol. The syntax used is:
Value1 - Value2
The value of Value1 is subtracted from the value of Value2. After performing the operation, a new value results. This result can be used in any way you want. For example, you can display it in a cell using the assignment operator as follows:
= Value1 - Value2
The multiplication allows adding one value to itself a certain number of times, set by the second value. The multiplication is performed with the * sign which is typed with Shift + 8. Here is an example:
Value1 * Value2
During the operation, Value1 is repeatedly added to itself, Value2 times. The result can be assigned to another value or displayed in a control as follows:
= Value1 * Value2
The division is used to get the fraction of one number in terms of another. For example, to divide a Value1 if Value2 pieces, you would use a syntax as:
Value1 / Value2
After performing the operation, you get a new result you can use as you see fit. You can display in a cell or involve it in an expression.
RTHS - Calculate the mean grade of each course (See Lesson 11)
Exponentiation is the ability to raise a number to the power of another number. This operation is performed using the ^ operator (Shift + 6). It uses the following mathematical formula:
The operation is performed as y^x and means the same thing. Either or both y and x can be values or expressions, but they must carry valid values that can be evaluated.
When the operation is performed, the value of y is raised to the power of x. You can display the result of such an operation in a cell using the assignment operator as follows:
You can also use the operation in an expression.
Parentheses are used to create sections in an expression. This regularly occurs when more than one operator is used in an operation. Consider the following expression typed in cell F2 as =8 + 3 * 5. The result of this operation depends on whether you want to add 8 to 3 then multiply the result by 5 or you want to multiply 3 by 5 and then add the result to 8.
Parentheses allow you to specify which operation should be performed first in a multi-operator operation. In our example, if you want to add 8 to 3 first and use the result to multiply it by 5, in the cell, you would write =(8 + 3) * 5. This would produce 55. On the other hand, if you want to multiply 3 by 5 first then add the result to 8, you would write 8 + (3 * 5). This would produce 23.
As you can see, results are different when parentheses are used on an operation that involves various operators. This concept is based on a theory called operator precedence. This theory manages which operation would execute before which one; but parentheses allow you to control the sequence of these operations.
Practical Learning: Using the Parentheses
So far in our expressions, we were selecting cells to combine their values to the operators and all the cells we used belonged to the same worksheet. In a typical workbook, you use various worksheet. Sometimes you will want want to a value stored in a cell of a separate worksheet and want to involve the value of that cell in the expression. Of course you can copy the value and paste it where needed. The problem is, when/if that value changes, you would have to change it in your expression. Instead of memorizing the value, you can create an expression that would directly use the value in its cell.
In Microsoft Excel, yon can create an expression that involves cells of two or more different worksheets. To proceed, in the cell where the expression will appear, type the assignment operator "=". If you know the name of the worksheet where the other cell is located, type that name. If the name of the worksheet is in more than one word, include it in single-quotes. If the name is in one word, you can omit the single-quotes. After the name of the worksheet, type the ! operator. If you want to use one cell, type its name. If you want to use a range of cells, type that range. If you want to use different non-adjacent cells, for each cell you want to use, type the name of the worksheet followed by ! and the name of the cell.
Instead of remembering the names of the worksheets and their cells, and as we have done so far with cells, you can start an expression with the = operator. Then, when you need a cell located in another worksheet, click the tab of that worksheet and select the cell. Microsoft Excel would take care of the names behind the scenes. When you end the expression, you will be taken back to the worksheet where you were working.
You may have one (or more) value(s) stored in the cell(s) of a (different) worksheet(s) and the worksheet(s) belong(s) to a different (or various) workbook(s). To use such a values, you could copy it and paste it in the cell that holds the expression you are creating. As mentioned for the worksheet, if that value changes, you would have to manually update the expression. Fortunately, you can create an expression that involves various workbooks and link them so that, when the value of an involved cell changes, the result of the expression would be automatically updated.
To involve the cell of a different workbook in an expression, start with the = operator. Type the name of the workbook as a file and, because it is a file, include its extension. Because the name of the workbook includes a period, you must start that name with the left square bracket "[" and you must end with the right square bracket "]". Just after the right square bracket, type the name of the worksheet where the cell is located. This name, whether the name of the worksheet is in one or more words, don't include it in single-quotes. Instead, the combination of the name of the workbook and the name of the worksheet must be included in single-quotes. After the the combination of the name of the workbook and the name of the worksheet, type the ! operator. As reviewed for the worksheet, the ! is followed by the name of the cell.
As done for the cells of one worksheet or a cell in a different worksheet, after starting the expression, you can access the other workbook and click the desired cell. If you use this technique (as opposed to typing the names), Microsoft Excel would start the name of the cell with $, followed by the letter-name of the cell, followed by $, and followed by the number of the row.
Practical Learning: Using Various Workbooks in an Expression
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