Experiment # 3 Combinational Circuits (I) Binary Addition and Subtraction

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Elwin Garrett
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1 Experiment # 3 Combinational Circuits (I) Binary Addition and Subtraction Objectives: 1. To study adder and subtractor circuits using logic gates. 2. To construct and test various adders and subtractor circuits. 3.1 Background: 1. Adders: Adder circuit is a combinational digital circuit that is used for adding two numbers. A typical adder circuit produces a sum bit (denoted by S) and a carry bit (denoted by C) as the output. Typically adders are realized for adding binary numbers but they can be also realized for adding other formats like BCD (binary coded decimal). Adder circuits are of two types: Half adders and Full adders. a. Half Adder Half adder is a combinational arithmetic circuit that adds two bits and produces a sum bit (S) and carry bit (C) as the output. If A and B are the input bits, then sum bit (S) is the X-OR of A and B and the carry bit (C) will be the AND of A and B. From this it is clear that a half adder circuit can be easily constructed using one X-OR gate and one AND gate. The truth table, and the XOR/AND realization of a half adder are shown in the figure below. The logic expressions for s and c are: Sum=A'B+AB' =A Carry=AB B Page 1

The Truth table and logic diagram of a 1 bit Full adder is shown below.

2 b. Full Adder: Full adder is a logic circuit that adds two input operand bits plus a Carry in bit and outputs a Carry out bit and a sum bit. The Sum out (Sout) of a full adder is the XOR of input operand bits A, B and the Carry in (Cin) bit. The Truth table and logic diagram of a 1 bit Full adder is shown below. A full adder can be implemented using two half adders as shown in the figure. Block diagram Logic expressions: Sum = A B Cin Carry = AB + Cin(A B ) Block diagram of full adder using two half adders Logic diagram of Full Adder Page 2

3 2. Subtractors: The subtraction of two binary numbers may be accomplished by taking the complement of the subtrahend and adding it to the minuend. By this method, the subtraction operation becomes an addition operation requiring full adders for its machine implementation. It is possible to implement subtraction with logic circuits in a direct manner. By this method, each subtrahend bit of the number is subtracted from its corresponding significant minuend bit to form a different bit. If the minuend bit is smaller than the subtrahend bit, a 1 is borrowed from the next significant position. The fact that a 1 has been borrowed must be conveyed to the next higher pair of bits by means of a binary signal coming out (output) of a given stage and going into (input) the next higher stage. a) Half Subtractor: 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). b) Full Subtractor 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) Page 3

4 3. Parallel Addition: In parallel addition, an n-bit parallel adder requires n full-adders, and all bits of X and Y are applied simultaneously. The output carry from one fulladder is connected to the input carry of the next full adder, the carry of the first stage is often considered as 0. As soon as the carries are generated, the correct sum bits emerge from the sum outputs of all full adders. 74LS83 74LS83 4-Bit Binary adder IC 1. Adder-Subtractor: In digital circuits, an adder subtractor is a circuit that is capable of adding or subtracting numbers (in particular, binary). Below is a circuit that does adding or subtracting depending on a control signal (s). when s=0 the circuit add binary number A to binary number B each of four bits resulting in SUM of four bit and output carry C4. When s=1 the circuit adds the 2 s complement of B to A resulting in difference S3 to S0 and C4 decided wither to complement the output result or not. \ Page 4

5 3.2 Prelab 1. Write down the truth table for each part in the labwork below 2. Draw pin connection diagram and function table of the binary adder 74ls83 Ic using data sheet. Parts list: KL trainer kit, lab module KL-33004, and 7483(binary adder). 3.3 Lab work: Part I : Half-Adder a) Construct the circuit of HA using module KL block a, connect inputs A and B to data switches and outputs F1 (carry) and F2 (sum) to LEDs, and do any other connections using clips. Record the truth table of the circuit and compare with that in your prelab. Page 5

6 Part II: Full-Adder Construct the circuit of FA using module KL block a, connect inputs A, B and C to data switches and outputs F3 (carry) and F5 (sum) to LEDs. and do any other connections using clips Record the truth table of the circuit and compare with that in your prelab. Part III: Subtractors Construct the circuit of HS and FS using module KL block a, connect inputs to data switches and outputs to LEDs, do the necessary connections. Record the truth tables of the two circuits and compare with that in your prelab. Part IV: 4-bit Parallel Adder using 74LS83 Use module KL block b to construct a 4-bit parallel adder Connect inputs X3~X0, and Y3~Y0 to DIP Switches DIP1: 3~0 and DIP2:3~0 respectively. Connect Y5(cin) to 0 for the circuit to act as adder. Connect Σ0, Σ1, Σ2, Σ3, C4 to LEDs L5~L1. Follow input sequences in the table below, record C4 and sum in hexadecimal numbers. Y X Σ F1 (carry) F F A B C E F F Page 6

7 Part V: 4-bit Parallel Subtractor using 74LS83 a) Repeat the steps in part 4 but connect Y5 to logic one this time for the circuit to act as a subtractor. b) Follow input sequences in the table below, record C4 and difference in hexadecimal numbers. According to the value of C4 decide if the output difference need to be complemented or not and explain why. Y X difference F1 (carry) Need to complement F F E 9 9 A B C E F F 3.4 Exercise 1. Design an 8 bit parallel adder using two ICs Show schematic diagram. 2. Design a BCD adder using two ICs Show in schematic diagram the circuit connections. Page 7

Experiment # 4. Binary Addition & Subtraction. Eng. Waleed Y. Mousa

Experiment # 4. Binary Addition & Subtraction. Eng. Waleed Y. Mousa Experiment # 4 Binary Addition & Subtraction Eng. Waleed Y. Mousa 1. Objectives: 1. To study adder and subtractor circuits using logic gates. 2. To construct and test various adders and subtractor circuits.