Combinational Logic. By : Ali Mustafa


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1 Combinational Logic By : Ali Mustafa
2 Contents Adder Subtractor Multiplier Comparator Decoder Encoder Multiplexer
3 How to Analyze any combinational circuit like this?
4 Analysis Procedure To obtain the output Boolean functions from a logic diagram: 1.Label all gate outputs that are a function of input variables. 2.Label the gates that are a function of input variables and previous labeled gates with different arbitrary symbols. 3.Repeat step 2 until the outputs of the circuit are obtained in terms of the input variables.
5 Analysis Procedure
6 Analysis Procedure
7 Analysis Procedure
8 Analysis Procedure Derivation of Truth Table
9 Analysis Procedure
10 Analysis Procedure
11 Summary : How to design a combinational circuit? 1. Determine the required number of inputs and outputs. 2.Derive the Truth Table. 3.Obtain the simplified Boolean functions. 4.Draw the logic diagram.
12 Example Design a combinational circuit with three inputs and one output. The output must equal 1 when the inputs are less than three and 0 otherwise. [use only NAND gates]
13 Example (cont.) 1The system have three inputs and one output
14 Example (cont.) 2 Derive the truth table
15 Example (cont.)
16 Circuits to be Implemented Arithmetic circuits Half Adder Full Adder Binary Adder/Subtractor Binary Multiplier Magnitude Comparator
17 What's the example of Arithmetic Circuit? One of the famous Digital Logic Circuits is the calculator.
18 Arithmetic circuits An arithmetic circuit is a combinational circuit that performs arithmetic operations such as addition, subtraction, multiplication and division with binary numbers or with decimal numbers in a binary code. A combinational circuit that performs the addition of two bits is called a Half Adder.
19 Half adder It is required to design a combinational circuit that adds two binary numbers and produce the output in the form of two bits sum and carry Solution 1 We need to determine the inputs and output of the system and give letters for all of them our system has two inputs (X, Y) and two outputs (S, C)
20 Half adder 2Derive the truth table according to the given relation between outputs and inputs In the half adder block the output equals the sum of two binary inputs
21 Half adder (cont.) 3 Obtain the simplified Boolean functions for each output as a function of the input variables using Kmap 4 Draw the logic diagram
22 Full Adder It is required to add three binary numbers Solution 1. From the specifications of the circuit, determine the required number of inputs and outputs and assign a letter (symbol) to each.
23 Full Adder (cont.) 2. Derive the truth table according to the given relation between outputs and inputs
24 Full Adder (cont.) 3 Obtain the simplified Boolean functions for each output as a function of the input variables using Kmap
25 Full Adder (cont.) 4 Draw the logic diagram
26 4Bit Binary Adder (Ripple Carry Adder)
27 Ripple Carry Adder
28 Binary Subtractor The subtraction of binary number can be done most conveniently by means of complements The subtraction AB is done by taking the 2 s complement of B and adding it to A. The 2 s complement can be obtained by taking the 1 s complement and adding 1 to the least significant bit. The 1 s complement can be implemented easily with inverter circuit and we can add 1 to the sum by making the initial input carry of the parallel adder equal to 1.
29 Adder/Subtractor
30 Subtractor A B D B A B C D B HALF SUBTRACTOR FULL SUBTRACTOR
31 Subtractor HALF SUBTRACTOR D = A B + AB B = A B FULL SUBTRACTOR D = A B C + A BC + AB C + ABC B = A C + A B + BC
32 4 Bit Subtractor
33 Assignment # 3 Design 4Bit Adder  Subtractor
34 4Bit Adder  Subtractor
35 Binary multiplier
36 Self Study 3 x 4 Bit Multiplier
37 Magnitude Comparator It is required to design a circuit to compare between two inputs A={A1,A0} and B={B1,B0} both inputs consists of two binary bits the circuit has three outputs Greater, Less, Equal
38 Magnitude Comparator (cont.) 1. Determine the required number of inputs and output.
39 Magnitude Comparator (cont.) 2. Derive the Truth Table that defines the required relationship between inputs and outputs.
40 Magnitude Comparator (cont.) 3 Get the simplified logic function of the outputs using kmap
41 Magnitude Comparator (cont.) 4 Draw the circuit
42 4 Bit Comparator
43 4 Bit Comparator
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