Arithmetic and Combinational Logic Circuits

Branch : Electronics & Communication Engg. Subject Duration : Digital Electronics : :Arithmetic and Combinational Logic Circuits : 100 min Sub Topic : 4-bit parallel Adder Topic 11 Objectives: On completion of this period, you will be able to understand • Implementation of 4-bit Parallel Adder using Full Adders. • Working of 4-bit Parallel Adder using Full Adders. SDE3204.36 to 37 2 2 Recap • What is a half adder? • A Half-Adder is a logic circuit that adds 2-binary bits. • What is full adder? • A Full-Adder is a logic circuit that adds 3-binary bits. • For both Full-Adder and Half-Adders there are two out puts Known as Sum and Carry. SDE3204.36 to 37 3 3 Truth Table of full adder SDE3204.36 to 37 4 4 4- Bit Parallel Adder Using Full Adders SDE3204.36 to 37 5 5 4-bit parallel adder • A binary adder is a logic circuit that can add two binary numbers. • The binary operation performed by the 4-bit parallel adder can be explained with the help of below example. Example: Let the two binary numbers that are to be added are C3 C2 C1 C0 Ci A3 A2 A1 A0 Ai B3 B2 B1 B0 Bi S3 S2 S1 S0 Si CS CR Cq CP Ci+1 SDE3204.36 to 37 6 6 Here, • A3 A2 A1 A0 = Ai is known as Augend. • Bi = B3 B2 B1 B0 is known as Addend. • Si = S3 S2 S1 S0 is known as sum. • Ci = C0 C1 C2 C3 is known as input carry. • Ci+1 = Cp Cq Cr Cs is known as output carry. SDE3204.36 to 37 7 7 4-bit parallel Adder using Full Adders: Fig. 1 SDE3204.36 to 37 8 8 • Fig 1 shows the inter connection of four full adders (FA) to implement a 4-bit parallel binary adder. • An n bit adder requires n Full Adders with each output carry connected to the input carry of the next higher order Full Adder. SDE3204.36 to 37 9 9 Working of 4-bit parallel adder using Full Adders • The working can be explained with two binary numbers that are to be added are A = 1 0 1 1 , B = 0 0 1 1 And input carry Ci = 0 1 1 0 • For the Full Adder (0) inputs are A0=1, B0=1 and C0=0. • It produces S0=sum=0; carry C1=1 SDE3204.36 to 37 10 10 • For the Full Adder(1) inputs are A1 = 1, B1= 1 and the carry from the Full Adder 1 is C1=1. • It produces S1= sum = 1, carry C2=1. • For the third Full Adder(2) inputs are A2=0,B2=0,C2=1. • It produces S2= sum =1 and carry C3= 0. SDE3204.36 to 37 11 11 • Similarly for the fourth Full Adder (3)inputs are A3=1 , B3=0 and C3=0. • It produces sum = S3=1 and carry = C4 =0 The above operation of 4-bit parallel Adder is shown in Table 1. SDE3204.36 to 37 12 12 If input carry = 0 1 1 0 = Ci Augend = 1 0 1 1 = Ai Addend = 0 0 1 1 = Bi Sum = 1 1 1 0 = Si Output carry = 0 0 1 1 = Ci+1 Table 1 SDE3204.36 to 37 13 13 Symbol of binary adder Fig 2 SDE3204.36 to 37 14 14 • As shown in symbol of binary adder A and B are added to get a sum of S plus a final carry. • By using more full adders, we can build binary adders of any length. • For example to add 16-bit numbers we need 16 Full Adders. SDE3204.36 to 37 15 15 Summary We have discussed 1. Implementation of 4-bit parallel Adder using Full Adders. 2. Working of 4-bit parallel Adder using Full Adders . SDE3204.36 to 37 16 16 QUIZ SDE3204.36 to 37 17 17 1. A logic circuit that can add two numbers (a) Binary Adder (b) Sub tractor (c) Inverter (d) None SDE3204.36 to 37 18 18 2. A logic circuit that accept 2 bits as input and produce their Sum and Carry outputs (a) Half Adder (b) Full Adder (c) Multiplier (d) All of the above SDE3204.36 to 37 19 19 3. A logic circuit that accepts two one bit signals and a carry in as inputs and produces their sum and carry as outputs (a) Half Adder (b) Full Adder (c) Both a and b (d) None SDE3204.36 to 37 20 20 4. An Adder circuit for adding multi bit numbers and accepting all the bits simultaneously (a) serial adder (b) parallel adder (c) both a and b (d) None SDE3204.36 to 37 21 21 Frequently Asked Questions 1. Implement 4-Bit parallel adder by using full adders. 2. Explain the working of 4-bit parallel adder by using full adders with a neat sketch. SDE3204.36 to 37 22 22