Page 58 - Digital Electronics by harish

It is constructed by cascading full adders one after another. Each full adder stage is
responsible for the addition of two binary digits and carry from the previous stage. The
carryout of one stage is fed directly to the carry-in of the next stage. x 3x 2x 1x 0 and y 3y 2y 1y 0 are
the data inputs, c 0 is the carry input, s 3s 2s 1s 0 is the sum output and c 4 is the carry output.

The augend‟s bits of „x‟ are added to the addend bits of „y‟ respectively of their binary
position. Each bit addition creates a sum s 0, s 1, s 2, s 3and a carry out c 1, c 2, c 3, c 4. The carry out
is then transmitted to the carry in of the next stage. The final result creates a sum of four bits
s 3s 2s 1s 0plus a carry out c 4.

2.7 Serial adder

Parallel adders are digital circuits that add „n‟ bits in serial, ie., one bit at a time. The logic
diagram of serial adder is shown in Figure.

Sum
Shift register A Full Shift register
A B Cout C
Adder
Cin

Q
Shift register D
B FF
Cloc CLK
k

Figure : Logic diagram of Serial adder

The shift register (right shift) A holds the augend bits (first numer) and shift register B holds
the addend bits (second number), after addition, the result will be avaialble in shift register C.
All the shift registers are right shift registers.The full adder performs the bit by bit addition.
The D-flip-flop is used to store the carry output generated after addition.

Initially, the D-flip-flip is cleared and addition starts with the least significant bits (LSBs) of
both shift registers. After each clock pulse, data within the shift registers A and B are shifted
right by 1-bit. The full adder adds the bits along with the carry of the previous state (from the
D flip-flop) and the sum is stored in the output shift register C.

2.8 BCD adder

A BCD adder is a circuit that adds two BCD digits and produces a sum digit in BCD format.
BCD numbers use 10 digits, 0 to 9 which are represented in the binary form 0000 to 1001,
(i.e.) each BCD digit is represented as a 4-bit binary number.

For adding two BCD numbers, the following procedure should be followed:

1. Add two BCD numbers using ordinary binary addition.
2. If the 4-bit sum is equal to or less than 9, no correction is needed. The sum is in proper
BCD form.

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