**Basic Theory:**

It
is possible to make a logical circuit that can do both addition and subtraction
based on the mode selection concept. In case of a four bit adder-subtractor,
two four bit binary numbers are added or subtracted on the basis of the
operation mode. The main principle behind it is subtraction using the two’s
complement method.

The expression for this is:

D

_{n}= A - B = A + B’ +1.
This
kind of circuit is a ripple-carry adder circuit along with some additional XOR
gates to add the subtraction functionality. It works as a full adder if the selected
mode is 0 “zero”, and works as a full subtractor if the mode is selected as 1
“one”. The logic diagram can be seen below.

**Circuit Diagram:**

**Observed Values:**

Following
set of values were obtained in observation.

For
addition,

1. 0011 + 0100 = 0111

2. 1101 + 0001 = 1110

3. 1101 + 0010 = 1111

4. 0010 + 0010 = 0100

5. 1000 + 1000 = 0000; Cout = 1

1. 0011 + 0100 = 0111

2. 1101 + 0001 = 1110

3. 1101 + 0010 = 1111

4. 0010 + 0010 = 0100

5. 1000 + 1000 = 0000; Cout = 1

For
subtraction,

1. 1011 – 1100 = 1111

2. 1010 – 0101 = 0101

3. 1111 – 1101 = 0010

4. 0011 – 0011 = 0000

5. 1000 – 0100 = 0100

1. 1011 – 1100 = 1111

2. 1010 – 0101 = 0101

3. 1111 – 1101 = 0010

4. 0011 – 0011 = 0000

5. 1000 – 0100 = 0100

**Reference:**

Wikipedia
(2013),

*Adder-subtractor*, Accessed: February 12, 2013, Retrieved from: http://en.wikipedia.org/wiki/Adder%E2%80%93subtractor
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