This preview shows page 1. Sign up to view the full content.
Unformatted text preview: osition. Two outputs are necessary because the sum of three binary digits
ranges in value from 0 to 3, and binary 2 and 3 need two digits. These two outputs are
designated by the symbols S (for sum) and C (for carry). The truthtable of Figure 6.38
exactly defines the function of fulladder. The l's and O's for the output variables are
determined from the arithmetic sum of the three input variables. When all input variables
are 0, the output is 0 for both C and S. The S output is equal to 1 when only one input is
equal to 1 or when all three inputs are equal to 1. The C output is 1 if two or three inputs
are equal to 1.
Inputs
Outputs
A
B
D
C
s
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
Figure 6.38. Truth table for a fulladder.
The sumofproducts expressions for the two outputs can be directly obtained from the
truth table and is given below:
Although the expression fcjr S cannot be simplified, it is possible to simplify the
expression for C as follows:
The S output from the second halfadder is the exclusiveOR of D and the output of the
first halfadder giving: S=(AB+AB]D+(AB+AB)D = AB AB D + ABD+ABD
= A + B • A + B D+ABD+ABD
=(A+B)(A+B)D+ABD+ABD
= (AA+AB+AB + BB)D+AB D+AB D
=(AB+ABJD+ABD+AB D = ABD+A§;D+AB D+AB D
= ABD+ABD+ABD+ABD
And we have the carry output
C = lAB + AB D + AB
= ABD+ABD+AB(D+D)
This can be simplified as before to C = AB + AD + BD
A Parallel Binary Adder
Parallel binary adders are used to add two binary numbers. For example, if we want to
add two fourbit numbers, we need to construct a parallel fourbit binary adder as shown
in Figure 6.41. Such an adder requires one halfadder (denoted by HA) and three fulladders (denoted by FA). The binary numbers being added are A 4 A3 A2 A! and B4 B3 B2
Bi and the answer is:
A4 A3 A2 A1,
+ B4 B3 B2B1,
S5 S4 S3 S2 S1
The first column requires only a halfadder. For any column above the first, there may be
a carry from the preceding column. Therefore, we must use a full adder for ea...
View
Full
Document
This document was uploaded on 04/07/2014.
 Spring '14

Click to edit the document details