An adder or summer is a digital circuit that performs addition of numbers. It is one of the most important components in a microprocessor. Adders are used not only in the arithmetic-logic-unit(ALU), but also in other parts of the processor, where they are used to calculate addresses, table indices, and similar. In this lab the students will design and build binary adder and subtractor circuits.
74LS83 4-Bit Binary full-adder
74LS86 Quad 2-input XOR Gate
74LS38 Quad 2-input OR Gate
74LS08 Quad 2-input AND Gate
A half adder adds two one-bit binary numbers A and B. It has two outputs, Sum and Carry (Represented by S and C). Carry is the value carried on to the next addition. The decimal value of the addition is 2*C + S. The simplest half-adder design incorporates an XOR gate for S and an AND gate for C. Half adders cannot be used to add more than 1 bit numbers due to no carry-in bit.
A-------+---\\ \
| )}XOR)---- S
B---+----)--// /
| |
| +--| \
| |AND)---- C
+------| /
Fig. 1 Half-adder circuit diagram
Table 1. Half-adder truth table
+----+----+
| AB | SC |
+----+----+
| 00 | 00 |
| 01 | 10 |
| 10 | 10 |
| 11 | 01 |
+----+----+
A full adder adds two binary digits A and B and a carry-in (Cin) from previous addition. The circuit produces a two-bit output sum typically represented by the signals C and S,
A-------+---\\ \
| )}XOR)--+
B---+----)--// / +-+-----\\ \
| | | )}XOR)---- S
Cin--)---)------+-------)----// /
| | | |
| | | +--| \
| | | |AND)--+
| | +---------| / |
| | +---\ \
| | ) OR )---- Cout
| | +---/ /
| +---------------| \ |
| |AND)---+
+--------------------| /
Fig. 1 Full-adder circuit diagram
Table 2. Full-adder truth table
A B Cin | Cout 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
The half-subtractor is a combinational circuit which is used to perform subtraction of two bits. It has two inputs, X (minuend) and Y (subtrahend) and two outputs D (difference) and B (borrow).
Table 3. Truth table of Half-subtractor, evaluating X-Y
XY BD
00 00
01 11
10 01
11 00
The full-subtractor is a combinational circuit which is used to perform subtraction of three bits. It has three inputs, X (minuend) and Y (subtrahend) and Z (subtrahend) and two outputs D (difference) and B (borrow).
Table 4. Truth table of Full-subtractor, evaluating X-Y-Z
XYZ BD
000 00
001 11
010 11
011 10
100 01
101 00
110 00
111 11
It is possible to create a logical circuit using multiple full adders to add N-bit numbers. Each full adder inputs a Cin, which is the Cout of the previous adder. This kind of adder is a ripple carry adder, since each carry bit "ripples" to the next full adder. Note that the first (and only the first) full adder may be replaced by a half adder.
A3 B3 A2 B2 A1 B1 A0 B0
| | | | | | | |
+-+----+-+ +-+----+-+ +-+----+-+ +-+----+-+
| FA.3 | | FA.3 | | FA.3 | | FA.3 |
Cout <--+ +<-Cin3 C2<--+ +<-Cin2 C1<--+ +<-Cin1 C0<--+ +<-- Cin
| | | | | | | |
+----+---+ +----+---+ +----+---+ +----+---+
| | | |
S3 S2 S1 S0
Pin# +--u--+ Pin#
A3 ( 1)--¦o ¦--(16) B3
S2 ( 2)--¦ 7 ¦--(15) S3
A2 ( 3)--¦ 4 ¦--(14) Cout
B2 ( 4)--¦ L ¦--(13) Cin
Vcc ( 5)--¦ S ¦--(12) Gnd
S1 ( 6)--¦ 0 ¦--(11) B0
B1 ( 7)--¦ 8 ¦--(10) A0
A1 ( 8)--¦ 3 ¦--( 9) S0
+-----+
Fig. Pin diagram of 74LS83 four bit adder
Implement the half adder circuit and verify the truth table.
Implement the 4-bit adder using 74LS83 and verify its truth table for upto random 10 inputs.
Design the 4-bit subtractor using 74LS83 and 74LS84. Verify its truth table for upto random 10 inputs.
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Circuit and Logic Diagram (3 points)
Simulation, Implementation and Working (3 points):
Experimental Results (3 points)
Critical Analysis and Conclusion (3 points)
Viva (3 points)