Can Two 8-bit Adders Be Used to Construct a 16-bit 2's Complement Adder?

[rgalvan2]

16 bit 2's complement adder. Due tomorrow!

You are given two adders. Each adder has two 8-bit operand inputs
and a 1-bit carry input. Each adder calculates the sum of the two
8-bit 2's complement operands and the 1-bit carry and outputs an 8-bit
sum and a 1-bit 2's complement overflow bit. Can you use the two
adders to create a 16-bit 2's complement adder? If so, draw it (represent
the adders as boxes with clearly labeled inputs and outputs). If not,
explain why it is difficult.

Help please

 

[MATLABdude]

Yes. The drawing and wiring are left as an exercise to the student :-)

HINT:
1) What happens to the 10s place when you add 15 and 27? What happened to the 1s place?
2) What is the purpose of the carry INPUT?

 

[piercas]

Yes, it is possible to use the two adders to create a 16-bit 2's complement adder. This can be achieved by cascading the two 8-bit adders together. The first adder will take the first 8 bits of the operands and the carry input, while the second adder will take the remaining 8 bits and the overflow bit from the first adder as the carry input. The output will be a 16-bit sum and a 1-bit overflow bit, which represents the 2's complement of the sum.

I have attached a diagram of the 16-bit 2's complement adder using the two 8-bit adders. Each box represents an 8-bit adder with clearly labeled inputs and outputs. The first adder takes in the first 8 bits of the operands (A0-A7) and the carry input (C0) and outputs an 8-bit sum (S0-S7) and an overflow bit (V0). The second adder takes in the remaining 8 bits of the operands (A8-A15) and the overflow bit (V0) from the first adder as the carry input (C1) and outputs the final 16-bit sum (S0-S15) and the overflow bit (V1).

It is not difficult to create a 16-bit 2's complement adder using these two 8-bit adders. However, it is important to note that this may not be the most efficient or optimal solution. There are other methods and circuits that can be used to create a 16-bit 2's complement adder with fewer components. It is always important to consider the trade-offs between complexity, cost, and performance when designing a circuit.