Page 44 - Computer_Science_F5

C = 2 AB (1 C+ 1 + C 1 ) C AB AB+ 1 ( + ) 3. Using the laws of Boolean algebra,
simplify the following expressions.
C = 2 AB C+ 1 (AB AB+ ) (a) AB+ AB+ BC + AC Chapter One: Computer architecture

C  2 AB C 1 (A ) B (b) A+ AB+C + BC
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The full adder can be simplified using the (c) A+ AB
two half adders, as shown in Figure 1.37. (d) ABC + AC + ABC
Half Adder
Half Adder
C 4. Given the Boolean expression
A 1 S Y = AB+ ABC + ABC + AB
B
(a) Draw the logic circuit of the
Boolean expression
(b) Simplify the Boolean
C
2 expression
Figure 1.37: Full adder logic circuit using two (c) Draw the logic circuit of the
half adders and OR gate simplified Boolean expression.
5. From the following Boolean
Exercise 1.7 expression, simplify and then draw
a logic circuit for the simplified
1. Draw the truth table of the half
adder and determine its Boolean expression.
expression. (a) Y = A(B+ AB)+ AC
2. Explain why Boolean algebra is (b) Y = A(A+ B)(A+ B)
important in the digital system. (c) Y = ABC+ ACC + ABC

Computer memory

Concept of computer memory

Scenario 1.3: Book storage in the library system

In any typical library, books are organised on shelves by subjects like Physics,
Mathematics, and Computer Science. This is similar to memory hierarchy in
computers, where data is stored at different levels based on accessibility and
speed. Signs and labels help people locate books easily, similar to memory
addresses used to access specific data on computers. Frequently accessed books
are placed closer for quick access, much like cache memory in computers
storing recently accessed data for faster retrieval. Books on shelves represent
primary memory for immediate access, while additional copies in storage rooms
or archives represent secondary memory.

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Student’s Book Form Five

Computer Science Form 5.indd 35 23/07/2024 12:32