Read the texts in Sections A and B and answer the questions.
Section A: For questions 1 - 5, choose the best option from a - d.
Binary logic consists of binary variables and logical operations. The variables are designated by letters of the alphabet such as A, B, C, x, y, z, etc., with each variable having two and only two distinct possible values: 1 and 0. There are three basic logical operations: AND, OR, and NOT.
AND: This operation is represented by a dot (.) or by the absence of an operator. For example, x.y=z or xy=z is read "X AND y is equal to z." The logical operation AND is interpreted to mean that z=1 if and only if x=1 and y= 1; otherwise z=0.
OR: This operation is represented by a plus sign (+). For example, x+y=z is read "X OR y is equal to z." meaning that z=1 if x=1 or if y=1 or if both x = 1 and y=1. If both x=0 and y=0, then z=0.
NOT: This operation is represented by a prime (') (sometimes by a bar). For example, x'=z (or ž = z) is read "x NOT is equal to z," meaning that z is what x is not. In other words, if x=1, then z=0; but if x=0, then z=1.
For each combination of the values of x and y, there is a value of z specified by the definition of the logical operation. These definitions may be listed in a compact form using truth tables.
A truth table is a table of all possible combinations of the variables showing the relation between the values that the variables may take and the result of the operation. For example, the truth tables for the operations AND and OR with variables x and y are obtained by listing all possible values that the variables may have when combined in pairs. The result of the operation for each combination will then be listed in a separate column. The truth tables below demonstrate the definitions of the operations, AND, OR, and NOT.
早稲田理工学部 2018-4 truth table
Binary logic diagrams are often used in the design of electronic circuits, where 1 represents a flowing current, and 0 represents no current. The operations are represented by logic gates, as in the diagram below, which perform a logical operation on one or more binary inputs, and produce a single binary output.
早稲田理工学部 2018-4 Binary Logic Diagram
[Adapted from Mano, M. Morris (1979) Digital Logic and Computer Design. Prentice Hall College Division.]
1. Which of the following is true about binary logic?
a. AND is equivalent to addition in arithmetic.
b. Logical operators have only one representation.
c. Variables can take on any positive value.
d. If z is a variable, then z=0 or z=1.
2. In the truth tables above, what are the values of the xy column when filled from the top to the bottom?
a. 0, 0, 0, 0
b. 0, 0, 0, 1
c. 0, 0, 1, 1
d. 0, 1, 1, 1
3. In the truth tables above, what are the values of the x+y column when filled from the top to the bottom?
a. 0, 0, 0, 0
b. 0, 0, 0, 1
c. 0, 0, 1, 1
d. 0, 1, 1, 1
4. What is the value resulting from the operations: (1・0)'+0?
a. 0
b. 1
c. 2
d. 10
5. When the output X of the electronic circuit is 0 in the binary logic diagram above, which of the following is a possible sequence of values for A, B, and C?
a. 0, 0, 0
b. 0, 1, 0
c. 0, 1, 1
d. 1, 1, 1
SectionB: For questions 6 -10, choose the best option from a - d.
Buying a property requires careful planning. Usually 10 percent of the property price should be paid first. The banks will loan the remaining 90 percent, which is called the principal. The expenses of purchasing and then living on the property are: the interest paid on the loan, purchasing expenses of 10 percent of the property price, and the property management fee. The money used to pay off the principal is not considered as an expense. We can calculate the total interest we will pay over t years, using the equations below.
(1) The total interest paid over t years = (The total payment made over t years) – (The principal paid off)
(2) The principal paid off = $ P-(Pr^t-A \frac{\large r^t-1}{\large r-1})$, where P is the principal, A is the yearly amount used to pay off the loan, r is the interest rate +1 (e.g., if the interest rate is 2, then r=0.02+1=1.02), and t is the number of years spent paying off the loan.
Calculating the cost of renting is much simpler. It merely involves summing the monthly expenditures (rent and management fee), any additional expenses such as key money, and a contract fee.
Now, let us consider the following property: A $ 20m^2 $ apartment, $ 20min $ from Waseda. The table below compares the approximate expenses of buying and renting the apartment in the first year (Year 1) and for the first four years (Years 1-4).
Buying
Price:15,000,000 yen.
Term of loan: 30 years.
Monthly management fee: 16,660 yen.
Loan interest rate (calculated annually, fixed over 30 years):2％.
Assume that the yearly amount to pay off the loan is 600,000 yen.
Renting
Monthly rent: 60,000 yen.
Monthly management fee: 5,000 yen.
Key money (one-timeonly): 65,000 yen.
Contract fee (renewed every two years): 65,000 yen.
早稲田理工学部 2018-4 Buying vs Renting
6. In the formula (2), what is P?
a. money borrowed from the bank
b. interest paid
c. deposit paid
d. property management fees
7. What is the approximate cost of renting in the first year?
a. 720,000
b. 800,000
c. 900,000
d. 1,500,000
8. What is the approximate cost of buying in the first year?
a. 1,500,000
b. 2,000,000
c. 2,500,000
d. 3,000,000
9. If a student bought the apartment upon entering Waseda University, approximately how much more would it cost in the four years until graduation than renting it?
a. 25,000
b. 250,000
c. 1,500,000
d. 3,000,000
10. Which of the following is true according to the text?
a. Buying is cheaper after one year, but the costs after six years are the same.
b. Renting is cheaper after one year, but the costs after six years are the same.
c. Buying is cheaper after one year, but renting is cheaper after six years.
d. Renting is cheaper after one year, but buying is cheaper after six years.
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