Page 41 - Computer_Science_F5

Computer Science Given the Boolean expression Creating Boolean expressions from
Example 1.11
logic circuits
You can create Boolean expressions from
AB .
ABC +
ABC +
AC +
the logic circuit by writing the expression
Y =
C FOR ONLINE READING ONLY
(a) Simplify the expression using
working to the last output. For example,
Boolean algebra for each gate at the leftmost inputs and
the Boolean expression of the logic circuit
(b) Draw the logic circuit of the in Figure 1.32, can be determined using
expression obtained in (a). the following steps:
Step 1: Simplify the Boolean expression A B (A B+ )BC

)BC
Y = AC (1 B+ ) AB+ (C + 1) B B (A B+ X
Y = AC .1 AB+ .1 C

Y = AC + AB Figure 1.32: Logic circuit

Y = ( A B C+ ) Step 1: The expression for left most
NOT gate with inputs A and B
Step 2: Determine the number of input is A and B , respectively.
variables A , B and C . Step 2: The output of the left most NOT
Step 3: Identify the operators required gates is the OR gate’s input.
in the expression. Therefore, the expression for

(a) One NOT gate is required OR gate is AB+ .
B . Step 3: The output of the OR gate
is one of the inputs to the
(b) One OR gate is needed to rightmost AND gate, and B and
combine C and B . C are other inputs. Therefore,
(c) One AND gate is required the expression for AND gate
for Aand BC+ , as shown is (A B+ )BC . The output
in Figure 1.31. expression for the entire logic
circuit is (A B+ )BC .
B B
B+C
Exercise 1.6

Y 1. Create a logic circuit of the Boolean
A expressions:
(a) AB BC+
Figure 1.31: Logic circuit for (b) BC + (B AC+ )

Y = A(B+C) (c) AB ABC+

32
for Advanced Secondary Schools

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