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Serial Binary Adder in Digital Electronics
In digital electronics, the binary adder is a combinational logic circuit which performs the addition of two or more binary digits. The binary addition is performed based on the Boolean algebraic laws of addition, i.e.,
$$0+0=0$$
$$0+1=1$$
$$1+0=1$$
$$1+1=0$$
Binary adders are classified into two types namely, serial binary adder and parallel binary adder.
In this tutorial, we will discuss serial binary adder, its definition, logic circuit diagram, and operation. So, let us start with basic introduction of serial binary adder.
What is a Serial Binary Adder?
A serial binary adder is a binary adder circuit which is used to add binary numbers in serial form. In the serial adder, the two binary numbers which are added serially are stored in two shift registers, let shift register A and shift register B.
The logic circuit diagram of the serial binary adder is shown in Figure 1.
The function of different elements of the serial adder circuit is as follows −
Full Adder − Full adder is a digital combinational logic circuit which can add three binary digits and can produce two output bits, i.e. sum bit and carry bit. In the serial binary adder circuit, the full adder adds one pair of bits at a time.
Shift Register − A group of flip-flops that can store several bits of data is called a shift register. In serial binary adder, two shift registers are used, where one is for storing augend bit and the other is for storing added of the binary number.
D Flip-Flop − In serial adder, the D flip-flop is used to store the carry output bit. The output of this D flip-flop is used as the carry input in the next stage of addition.
Operation of Series Binary Adder
In the serial binary adder circuit, the binary digits (bits) are added one pair at a time using a full-adder circuit. The carry generated from the full adder is transferred to a D-flip flop. Thus, the output of this D-flip flop is then used as the carry input for the next pair of significant bits. The sum bit S is transferred to a third shift register. Now, let us understand the operation of the serial binary adder in the detail.
At beginning, the shift register A stores the augend bit of the given binary number, and the shift register B stores the addend bit. Initially, the D flip flop is cleared to 0, hence no carry bit is present. The outputs of shift registers A and B supply a pair of significant bits to the full adder circuit at inputs I0 and I1. A shift control is used to enable the shift registers A and B and the carry flip-flop. Therefore, at each clock pulse, the registers A and B are shifted to the right, and the sum bit from output S of the full adder circuit enters the left most of the shift register A. Thus, for each succeeding clock pulse a new sum bit is transferred to the shift register A and a new carry bit is transferred to the output Q of the D flip flop. This process continues until the shift control is disabled.
Hence, the addition of two binary numbers in serial form is accomplished by supplying a pair of bits together with the previous carry to a full adder circuit, and transferring a sum bit at a time into the shift register A.
Now, we can summarize the working process of the serial binary adder as follows −
Initially, the shift register A and the carry flip flop are set to 0, and the first number is added from the register B.
When the register B is shifting through the full adder, a second number is transferred to it through its serial input.
This second number is then added to the number of the register A, while a third number is transferred to into the register B through the serial input.
This process is executed repeatedly to perform the addition of two, three, or more binary number in serial form and accumulate the sum result in the shift register A.
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