Page 417 - Engineering Digital Design

PROBLEMS 387

greater than 9 but less than 19. Then use one of two 4-bit adders (as shown) to add
01 10 to the sum conditionally on X. Note the logic symbol for the 1 -digit BCD
adder in Fig. P8.2b. What restrictions, if any, are placed on the operands?
(b) Test the design of a two-digit BCD adder by adding the following two BCD
numbers:

Test#l A = 9i 0 ;£ = 7, 0
Test #2 A = 34i 0;5 = 19 10
To do this, indicate the logic values for each sum, carry, and correction parameter
X.
8.12 (a) Alter the design of Problem 8.11 with the appropriate external logic so as to
create a one-digit BCD adder/subtractor that can be bit-sliced to form an n-digit
BCD adder/subtractor, all with B as the subtrahend. (Hint: Add an enable EN(H)
= A/S(H) mode control to the correction logic of Problem 8.11 and use 10's
complement arithmetic to perform BCD subtraction operations. To do this, fol-
low Fig. 8.9 with the appropriate external logic on the input for cascading pur-
poses. Also, remember that a 1 carry cannot be generated in BCD subtraction.
It is important to note that, in this case, the negative number is not converted to
10's complement as in Algorithm 2.15, which is an alternative means of BCD
subtraction.)
(b) Test the design of a two-digit BCD adder/subtractor by introducing the following
numbers and mode control:

Test #1 A = 610, B = 29io, and A/S(H) =
Test #2 A = 6,0, B = 29, 0, and A/S(H) = l(H)

To do this, indicate the logic values for each operand, sum, carry, mode control, and
correction parameter. Note that if the result of a subtraction is a negative number,
it will be represented in 10's complement, and that its true value can be found by
negation of each digit separately.
8.13 Use two 4-bit binary adders and the necessary correction and external logic to design
a one-digit XS3 adder (similar to BCD adder in Fig. P8.2) that can be cascaded to
form an n-digit XS3 adder. To do this, use the following algorithm:

Add XS3 numbers by using binary addition: If there is no 1 carry from the 4-bit sum,
correct that sum by subtracting 0011 (3io). If a 1 carry is generated from the 4-bit
sum, correct that sum by adding 0011. Remember that XS3 numbers less than 3 or
greater than 12 are not used and that the sum of two XS3 numbers cannot exceed 24 10.

[Hint: First, find the minimum logic for the correction parameter X that will indicate
when the sum is greater than 12 but less than 25, the range over which a 1 carry is
generated. Also, controlled inverters (XOR gates) must be used for the addition or
subtraction of SIQ.] What restrictions, if any, are placed on the operands?
8.14 (a) Alter the design of Problem 8.13 so as to create a one-digit XS3 adder/subtractor
that can be cascaded to form an n-digit XS3 adder/subtractor, all with B as the