n bit binary adder or ripple carry adder

By using full adder, a single 1-bit binary adders can be constructed from basic logic gates as shown below

But what if we wanted to add together two n-bit numbers, then n number of 1-bit full adders need to be connected or “cascaded” together to produce a adder known as a Ripple Carry Adder.

Ripple carry adder is simply “n“ number of 1-bit full adders cascaded together with full adder representing a single weighted column in a long binary addition. It is called a ripple carry adder because the carry signals produce a “ripple” effect through the binary adder from LSB to MSB.

Let us consider a three bit full adders to “add” together two 3-bit numbers, the two outputs of the first full adder will provide the first place digit sum (S) of the addition plus a carry-out bit that acts as the carry-in digit of the next binary adder. The second binary adder in the chain also produces a summed output (the 2nd bit) plus another carry-out bit and we can keep adding more full adders to the combination to add larger numbers, linking the carry bit output from the first full binary adder to the next full adder, and so forth. An example of a 3-bit adder is given below.

Let us consider A =4 , B=3, sum of A and B will be 7. In binary addition

There will be a overflow ,If the sum was greater than or equal to 2ⁿ one of the disadvantage in this adder. Let us consider A =4 , B=4, Sum of A and B will be 8 which is equal to 2³ and we will have a overflow .

There two main disadvantages in ripple carry adder

• Propagation delay:
  if inputs A and B changes, the sum at its output will not be valid until any carry-input has “rippled” through every full adder in the chain because the MSB of the sum has to wait for any changes from the carry input of the LSB. Consequently, there will be a finite delay before the output of the adder responds to any change in its inputs resulting in a accumulated/propagation delay. This delay can be neglected for 4 to 8 bits but we cannot neglect the delay for higher bits like 32 bits and more.
• Over flow:
  Overflow occurs when the two n bit numbers add together whose sum is greater than or equal to 2ⁿ

To reduce the propagation delay of carry_in we can use Carry Look Ahead Binary Adder

CHISEL: Counter in Chisel

In digital systems counter is plays a main role. Counters are used to keep a track of events , time intervals and no of interrupts etc. . Counter can be programmed in many languages like verilog, c , c++ , java, python, chisel etc. In this post we will see how to program a counter in chisel language.

Design a counter which starts counting from 0 till 9 and reset to 0 once it counts till 9.

val cntSpace = RegInit (0.U (8.U))—> defines a 8 bit register which initialize to 0 upon reset signal
cntSpace := Mux( cntSpace ===9.U , 0.U, cntSpace + 1.U)

:= ——> update register
When the cntSpace reaches to 9, it will initialize to 0 otherwise the cntSpace will be incremented by one

scan cell, scan chain

Scan cell is one of the DFT technique , to test the sequential circuits in the Asic/Soc design. Normal D flip flop are converted to scan flip flop, if the tool meets the following criteria

• Clock of the flip flop must be controllable
• The set/reset of the flops must be inactive during the shift mode.

Once the all the flops in the design meet the above two rules the tool will convert the d flops to scan flops by adding a mux as shown in figure above. Then the tools will stitch the scan cells into a scan chain according to the design requirements.

When Scan Enable is 0 (SE=0), all the scan chains in the design will be disconnected and the flops are connected to comb. logic

When Scan Enable is 1 (SE=1) , combinational logic will be bypassed and all scan cells will be connected to form a scan chain

When SE=1 , patterns are loaded to the scan chains and the data from the comb logic are captured when SE=0

scan chain REORDERING , why it is required

Scan chain reordering is an optimization technique to ensure scan chains are connected in more efficient way – based upon the placement of the flip-flops. At initial stage , we donot have the placement information, so we just stitch the flops register by register. The tools will stitch the flops randomly to form a scan chain before placement. For proper understanding flops are numbered and two scan chains are stitched in the screen shot shown below.

But after placement it might be possible that the two flops stitched at initial stage of a different block sits far from each other when the placement is done. So if we keep the same scan chain order, we will face the placement congestion and timing congestion and more routing resources are required.

We can see from above screenshot, depending on the timing and placement congestion flops are placed at different locations when compared to before placement figure. This results in usage of more resources, space congestion increases and also timing violations. By reordering the scan cells in the scan chain we can reduce the congestion

In order to avoid the congestion before placement we have to follow the below steps

• Disconnect the scan chain in the designing.
• Based on the timing and congestion the tool optimizes the standard cells
• Once the placement was done, reordering of scan chains are done based on the timing and placement congestion in design by maintaining the same number of scan cells .

SCANDEF file contains the scan chain information of the design and this file need to be read during PnR.