Page 42 - Computer_Science_F5

2. Determine the Boolean expression a half adder can be overcome using a full
and draw the truth table from the adder. The full adder is the logic circuit
following circuit in Figure 1.33 with a condition to add a carry. Therefore, Chapter One: Computer architecture

A it adds three binary digits together. Adders
are the circuits within the ALU in the CPU
FOR ONLINE READING ONLY
that perform binary addition. Therefore,
B
F they are vital circuits used in computers
for number addition.
C
Figure 1.33: Determining Boolean expression
Construction of half adder
3. Design a combinational circuit This simple addition consists of four
with three input A, B, and C and possible operations which are:
three outputs X, Y, and Z. When 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and
the binary input is 0, 1, 2, and 3 the 1 + 1 = 10.
binary output is too greater than the
input, when the binary input is 4, 5, The first three operations result in a single-
6, 7, the binary output is three less digit sum while the fourth operation results
than the input. in a two-digit sum. A carry is the most
(a) Construct a truth table for that significant bit in this operation. As a result,
scenario. the first three operations carry ‘0’ whereas
(b) Derive the Boolean expression the fourth produces a carry of ‘1’. Table
for the output. 1.12 shows the truth table for the Boolean
(c) Simplify the Boolean realisation of the binary addition.
expression for output obtained
in part (b). Table 1.12: Half adder Table
(d) Draw a logic circuit for that Input Output
simplified expression in part (c).
A B Sum(S) Carry (C)

Construction of half and full adder 0 0 0 0
An adder is a digital circuit that adds 0 1 1 0
binary values together. Adders are used 1 0 1 0
in many computers and other types 1 1 0 1
of processors to execute a variety of
computations such as calculating address From the truth table, you obtain the
table indices in the ALU. There are two Boolean expression for S and C as follows:
types of adders, namely half adder and S  AB AB  A B and C = AB
full adder. A half adder is a logic circuit
that adds two binary digits together. The The Boolean expressions show that
half adder has two outputs which are the sum and carry are equivalent to XOR
Sum (S) and Carry (C). This limitation of and AND gate, respectively. The logic

33
Student’s Book Form Five

Computer Science Form 5.indd 33 23/07/2024 12:32