Parallel Adder and Parallel Subtractor

Adding and Subtracting numbers is very simple in digital electronics. To do this for quickly and efficiently, Most of the for binary numbers (numbers made of 1 and 0), we use circuits like the Parallel Adder and Parallel Subtractor. These types of circuits can handle more than one bit at a time, making the process faster.

Binary Addition

Binary addition works sane as a to regular addition, but it only uses two digits: 0 and 1.

Always remember this in your mind

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 10 (1 is a carry)

Example

We are working on 13 = 1 1 0 1 and 11 = 1 0 1 1

1 1 0 1 + 1 0 1 1 ──────────── 1 1 0 0 0

So, the final answer is 11000, If we convert in a decimal so answer is 24.

Binary Subtraction

Binary subtraction is a same as regular subtraction, but with binary numbers. We mostly use a method called 2’s complement to make subtraction simple.

Steps for Binary Subtraction:

Find the 1’s complement of the factor ( You need to do like this 0 to 1 and 1 to 0).

Add 1 in the 1’s complement, and you will get the 2’s complement.

Add the 2’s complement to the minuend.

Example:

Now we are adding 13 and 11

1 1 0 1 – 1 0 1 1 ▔▔▔▔ 0 0 1 0 = 2

How it works

• Find the 1’s complement of 1011: 0100.
• Add 1 to get the 2’s complement: 0101.
• Now, add it to the minuend:

1 1 0 1 + 0 1 0 1 ───── 1 0 0 1 0

At this time we are working on 4 bit numbers, we ignore the carry, so the result is 0010 (this binary means 2 in decimal).

Parallel Adder

A single full adder performs the addition of two one bit numbers and an input carry. But a Parallel Adder is a digital circuit capable of finding the arithmetic sum of two binary numbers that is greater than one bit in length by operating on corresponding pairs of bits in parallel. It consists of full adders connected in a chain where the output carry from each full adder is connected to the carry input of the next higher order full adder in the chain.

A n bit parallel adder requires n full adders to perform the operation.

So for the two-bit number, two adders are needed while for four bit number, four adders are needed and so on. Parallel adders normally incorporate carry lookahead logic to ensure that carry propagation between subsequent stages of addition does not limit addition speed.

Working of Parallel Adder

1. As you can show in the figure, first of all the full adder FA1 add A1 and B1 along with the carry C1 to generate the sum S1 (the first bit of the output sum) and the carry C2 which is connected to the next adder in chain.
2. Next, the full adder FA2 uses this carry bit C2 to add with the input bits A2 and B2 to generate the sum S2(the second bit of the output sum) and the carry C3 which is again further connected to the next adder in chain and so on.
3. The process continues till the last full adder FAn uses the carry bit Cn to add with its input An and Bn to generate the last bit of the output along last carry bit Cout.

Parallel Subtractor

A Parallel Subtractor is a digital circuit capable of finding the arithmetic difference of two binary numbers that is more than one bit in length by operating on pairs of bits in parallel. The parallel subtractor can be designed in several ways including combination of half and full subtractors, all full subtractors or all full adders with the complement of the number being subtracted input.

Working of Parallel Subtractor

1. As shown in the figure, the parallel binary subtractor is formed by combination of all full adders with subtrahend complement input.
2. This operation considers that the addition of minuend along with the 2’s complement of the subtrahend is equal to their subtraction.
3. Firstly the 1’s complement of B is obtained by the NOT gate and 1 can be added through the carry to find out the 2’s complement of B. This is further added to A to carry out the arithmetic subtraction.
4. The process continues till the last full adder FAn uses the carry bit Cn to add with its input An and 2’s complement of Bn to generate the last bit of the output along last carry bit Cout.

Advantages of parallel Adder/Subtractor

1. The parallel adder/subtractor performs the addition operation faster as compared to serial adder/subtractor.
2. Time required for addition does not depend on the number of bits.
3. The output is in parallel form i.e all the bits are added/subtracted at the same time.
4. It is less costly.

Disadvantages of parallel Adder/Subtractor

1. Each adder has to wait for the carry to come from the previous adder in the chain.
2. The propagation delay( delay associated with the travelling of carry bit) is found to increase with the increase in the number of bits to be added.

Conclusion

Parallel Adders and Parallel Subtractors are special circuits used in digital electronics to add and subtract binary numbers faster. They are faster because they handle multiple bits at the same time. While they have some advantages, like speed, they also have control, such as the delay caused by carrying bits from one adder to another adder.