How To Understand Ex3 Sum Mechanism?

[some_one]

i need to implement a circuit that inputs two 4bit numbers (y3 y2 y1 y0 x3 x2 x1 x0)
and it has an output of (c3 c2 c1 c0 s3 s2 s1 s0) where "c" is the carry
and "s" is the sum

i was given an example in which X=0101 (5) Y=1000 (8) and it outputs
S=1010 (10) and C=0011 (3)
5+8=13

i don't know what is the role of C and S
how do they split the numbers?

i was asked to implement it using two 4 bit adders

here is the answer:

htp://img116,imageshack,us/my,php?image=img8831gx1,jpg

i can't understand this circuit
?

 

[KataKoniK]

The role of C and S in this circuit is to represent the carry and sum of the two 4-bit numbers that are being added together. In the example given, the numbers 5 and 8 are being added together, resulting in the sum of 13. This sum is represented by the 4 bits in the output labeled as S (s3 s2 s1 s0).

The carry (c3 c2 c1 c0) represents any carry that occurs during the addition process. In this case, the carry is 1 in the first and third bit positions, indicating that there was a carry from the first and third bit positions of the input numbers.

The circuit provided in the answer uses two 4-bit adders to add the two input numbers together. The first adder adds the first and second bits of the inputs, while the second adder adds the third and fourth bits. The outputs of these two adders are then combined to produce the final sum and carry outputs.

I understand that the circuit may be difficult to understand at first glance, but it is a common way to implement a 4-bit adder using two smaller adders. I suggest studying the circuit in more detail and researching how 4-bit adders are typically implemented to gain a better understanding.

I hope this helps clarify the role of C and S in this circuit and how it is implemented using two 4-bit adders. Let me know if you have any further questions. Good luck with your project!

 

[piercas]

I can provide a technical explanation for understanding the Ex3 Sum Mechanism. This mechanism is used to perform addition between two 4-bit numbers and produce a 4-bit sum and a 4-bit carry. The circuit shown in the provided link is an implementation of this mechanism using two 4-bit adders.

The inputs to the circuit are two 4-bit numbers, represented as y3 y2 y1 y0 and x3 x2 x1 x0. These are the binary representations of the two numbers that need to be added. The output of the circuit is a 4-bit sum, represented as s3 s2 s1 s0, and a 4-bit carry, represented as c3 c2 c1 c0.

The role of the carry, represented as c3 c2 c1 c0, is to hold any carryover from the previous addition operation. In the example given, the carry value is 0011, which means there was a carryover of 1 from the first addition of 0+0. This carry value is then added to the next addition of 1+0, resulting in a sum of 1 and a carry value of 0.

The role of the sum, represented as s3 s2 s1 s0, is to hold the actual sum of the two numbers being added. In the example given, the sum value is 1010, which is the binary representation of the decimal number 10. This means that the sum of the two numbers 5 and 8 is 10.

To understand how the numbers are split, we need to look at the circuit diagram. Each 4-bit number is split into four individual bits, which are then fed into the two 4-bit adders. The outputs of the two adders are then combined to produce the final 4-bit sum and carry values.

In summary, the Ex3 Sum Mechanism is a circuit that performs addition between two 4-bit numbers and produces a 4-bit sum and carry value. The carry value represents any carryover from the previous addition, while the sum represents the actual sum of the two numbers. The numbers are split into individual bits and fed into two 4-bit adders, which are then combined to produce the final output.