Digital Logic Design PDF

DIGITAL LOGIC DESIGN Engr. Abdul Jalil  ADDER Addition is one of the most basic operations performed by different electronic devices like computers, calculators, etc. The electronic circuit that performs the addition of two or more numbers, more specifically binar...

DIGITAL LOGIC DESIGN Engr. Abdul Jalil  ADDER Addition is one of the most basic operations performed by different electronic devices like computers, calculators, etc. The electronic circuit that performs the addition of two or more numbers, more specifically binary numbers, is called as adder. Since, the logic circuits use binary number system to perform the operations, hence the adder is referred to as binary adder  HALF-ADDER A combinational logic circuit which is designed to add two binary digits is called as a half adder. The half adder provides the output along with a carry value (if any). The half adder circuit is designed by connecting an EX-OR gate and one AND gate. It has two input terminals and two output terminals for sum and carry. The block diagram and circuit diagram of a half adder are shown in Figure-1.  HALF-ADDER  OPERATION OF HALF ADDER Half adder adds two binary digits according to the rules of binary addition. These rules are as follows − 0+0=0 0+1=1 1+0=1 1+1=10(Sum=0&Carry=1) According to these rules of binary addition, we can see that the first three operations produce a sum whose length is one digit, whereas in the case of last operation (1 and 1), the sum consists of two digits. Here, the MSB (most significant bit) of this result is called a carry (which is 1) and the LSB (least significant bit) is called the sum (which is 0).  TRUTH TABLE OF HALF ADDER  K-MAP FOR HALF ADDER We can use the K-Map (Karnaugh Map), a method for simplifying Boolean algebra, to determine equations of the sum bit (S) and the output carry bit (C) of the half adder circuit. CHARACTERISTIC EQUATIONS OF HALF- ADDER The characteristic equations of half adder, i.e., equations of sum (S) and carry (C) are obtained according to the rules of binary addition. These equations are given below  APPLICATIONS OF HALF ADDER Half adder is used in ALU (Arithmetic Logic Unit) of computer processors to add binary bits. Half adder is used to realize full adder circuit. Half adder is used in calculators. Half adder is used to calculate addresses and tables.  FULL ADDER A combinational logic circuit that can add two binary digits (bits) and a carry bit, and produces a sum bit and a carry bit as output is known as a full-adder. a combinational circuit which is designed to add three binary digits and produces two outputs (sum and carry) is known as a full adder. Thus, a full adder circuit adds three binary digits, where two are the inputs and one is the carry forwarded from the previous addition.  FULL ADDER the circuit of the full adder consists of one EX-OR gate, three AND gates and one OR gate, which are connected together as shown in the full adder circuit in Figure TRUTH TABLE OF FULL ADDER  K-MAP FOR FULL ADDER K-Map (Karnaugh Map) is a tool for simplifying binary complex Boolean algebraic expressions. CHARACTERISTIC EQUATIONS OF FULL ADDER The characteristic equations of the full adder, i.e. equations of sum (S) and carry output (Cout) are obtained according to the rules of binary addition.  ADVANTAGES OF FULL ADDER Full adder provides facility to add the carry from the previous stage. The power consumed by the full adder is relatively less as compared to half adder. Full adder can be easily converted into a half subtractor just by adding a NOT gate in the circuit. Full adder produces higher output that half adder. Full adder is one of the essential part of critic digital circuits like multiplexers. Full adder performs operation at higher speed.  APPLICATIONS OF FULL ADDER Full adders are used in ALUs (arithmetic logic units) of CPUs of computers. Full adders are used in calculators. Full adders also help in carrying out multiplication of binary numbers. Full adders are also used to realize critic digital circuits like multiplexers. Full adders are used to generate memory addresses. Full adders are also used in generation of program counterpoints. Full adders are also used in GPU (Graphical Processing Unit). END OF LECTURE