Digital Design
Tutorial Sheet 6
September 27, 2023
Digital Design
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Problem - 1
a)
b)
c)
Consider the Adder - Subtractor block shown below. Can this block be used for
both signed and unsigned numbers? If so, how would the interpretation of the
inputs and outputs change?
What is the difference between carry and overflow? What do each of them
signify in the context of addition.
Give the values of S3, S2, S1, S0, C and V for the following input values and
also write the decimal equivalent of both the inputs and outputs considering
unsigned inputs.
1) A = 1100, B = 1001 and M = 0
2) A = 0101, B = 1010 and M = 1
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Answer
(a) Yes, the block can be used for operating on both signed and unsigned numbers.
Unsigned : The inputs are fed in their normal binary representation, with M = 0
performing unsigned addition and M = 1 performing unsigned subtraction. The
result of the addition can simply be interpreted in binary format. For subtraction,
if A>B, the result is in binary representation, whereas if A<B, the result
represents the 2’s complement of B-A.
The range of output for n bit block : [0, 2n - 1]
Signed : Both the inputs and outputs should be interpreted in the 2’s
complement format.
The range of output for n bit block : [-2(n-1), 2(n-1) - 1]
(b) Overflow is said to occur for an n bit block of the result cannot be represented in
n bits.
Unsigned Addition : The overflow is simply the carry bit.
Signed Addition : The carry bit does not represent an overflow here, the V bit
does. Overflow can only occur if both the numbers we are adding are positive,
or both are negative.
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Solution
1.
A = 12, B = 5, {C,S} = 21
S3 = 0, S2 = 1, S1 = 0, S0 = 1, C = 1, V = 1
2.
A = 5, B = 10, S = 11 (unsigned) = -5 (signed)
S3 = 1, S2 = 0, S1 = 1, S0 = 1, C = 0, V = 1
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Problem - 4
a) Give the truth table of full subtractor?
b) Design the same using full adder?
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Solution
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Solution
A
S
B
FA
C
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B
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Problem 5
Q1. Design a combinational circuit that subtracts a
constant ‘2’ from a 3-bit number using 3 number
of Full adder and additional required gates.
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Solution
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Problem 6
(a) Derive the Boolean expressions for T1 to
T4. Evaluate the outputs F1 and F2 as a
function of four inputs, A, B, C and D
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Problem 6
(b) Make the truth table for inputs A,B,C & D
and outputs T1 to T4, F1 & F2.
(c) Plot the Boolean output functions
obtained in (b) on K-maps
(d) Show that the simplified Boolean
expressions are equivalent to the ones
obtained in (a).
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Solution
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Solution 4
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Solution 4
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Alternate way of covering
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Thank you
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