Tree Adder Delay Solution

STEP 0: Pre-Calculation Summary
Formula Used
Tree Adder Delay = Propagation Delay+log2(Absolute Frequency)*AND-OR Gate Delay+XOR Delay
ttree = tpg+log2(fabs)*Tao+Txor
This formula uses 1 Functions, 5 Variables
Functions Used
log2 - The binary logarithm (or log base 2) is the power to which the number 2 must be raised to obtain the value n., log2(Number)
Variables Used
Tree Adder Delay - (Measured in Second) - Tree Adder Delay is the delay in the circuit and is denoted by Ttree symbol.
Propagation Delay - (Measured in Second) - Propagation delay typically refers to the rise time or fall time in logic gates. This is the time it takes for a logic gate to change its output state based on a change in the input state.
Absolute Frequency - (Measured in Hertz) - Absolute Frequency is the number of occurrences of a particular data point in a dataset. It represents the actual count or tally of how many times a specific value appears in the data.
AND-OR Gate Delay - (Measured in Second) - AND-OR Gate Delay in the gray cell is defined as the delay in the computing time in AND/OR gate when logic is passed through it.
XOR Delay - (Measured in Second) - XOR Delay is the propagation delay of XOR gate.
STEP 1: Convert Input(s) to Base Unit
Propagation Delay: 8.01 Nanosecond --> 8.01E-09 Second (Check conversion here)
Absolute Frequency: 10 Hertz --> 10 Hertz No Conversion Required
AND-OR Gate Delay: 2.05 Nanosecond --> 2.05E-09 Second (Check conversion here)
XOR Delay: 1.49 Nanosecond --> 1.49E-09 Second (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ttree = tpg+log2(fabs)*Tao+Txor --> 8.01E-09+log2(10)*2.05E-09+1.49E-09
Evaluating ... ...
ttree = 1.63099525945191E-08
STEP 3: Convert Result to Output's Unit
1.63099525945191E-08 Second -->16.3099525945191 Nanosecond (Check conversion here)
FINAL ANSWER
16.3099525945191 16.30995 Nanosecond <-- Tree Adder Delay
(Calculation completed in 00.004 seconds)

Credits

Created by Shobhit Dimri
Bipin Tripathi Kumaon Institute of Technology (BTKIT), Dwarahat
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19 Array Datapath Subsystem Calculators

Carry-Looker Adder Delay
Go Carry-Looker Adder Delay = Propagation Delay+Group Propagation Delay+((N-Input AND Gate-1)+(K-Input AND Gate-1))*AND-OR Gate Delay+XOR Delay
Multiplexer Delay
Go Multiplexer Delay = (Carry-Skip Adder Delay-(Propagation Delay+(2*(N-Input AND Gate-1)*AND-OR Gate Delay)-XOR Delay))/(K-Input AND Gate-1)
Carry-Skip Adder Delay
Go Carry-Skip Adder Delay = Propagation Delay+2*(N-Input AND Gate-1)*AND-OR Gate Delay+(K-Input AND Gate-1)*Multiplexer Delay+XOR Delay
Carry-Increamentor Adder Delay
Go Carry-Incrementor Adder Delay = Propagation Delay+Group Propagation Delay+(K-Input AND Gate-1)*AND-OR Gate Delay+XOR Delay
Critical Delay in Gates
Go Critical Delay in Gates = Propagation Delay+(N-Input AND Gate+(K-Input AND Gate-2))*AND-OR Gate Delay+Multiplexer Delay
Group Propagation Delay
Go Propagation Delay = Tree Adder Delay-(log2(Absolute Frequency)*AND-OR Gate Delay+XOR Delay)
Tree Adder Delay
Go Tree Adder Delay = Propagation Delay+log2(Absolute Frequency)*AND-OR Gate Delay+XOR Delay
Cell Capacitance
Go Cell Capacitance = (Bit Capacitance*2*Voltage Swing on Bitline)/(Positive Voltage-(Voltage Swing on Bitline*2))
Bit Capacitance
Go Bit Capacitance = ((Positive Voltage*Cell Capacitance)/(2*Voltage Swing on Bitline))-Cell Capacitance
Voltage Swing On Bitline
Go Voltage Swing on Bitline = (Positive Voltage/2)*Cell Capacitance/(Cell Capacitance+Bit Capacitance)
Ground Capacitance
Go Ground Capacitance = ((Agressor Voltage*Adjacent Capacitance)/Victim Voltage)-Adjacent Capacitance
'XOR' Delay
Go XOR Delay = Ripple Time-(Propagation Delay+(Gates on Critical Path-1)*AND-OR Gate Delay)
Carry-Ripple Adder Critical Path Delay
Go Ripple Time = Propagation Delay+(Gates on Critical Path-1)*AND-OR Gate Delay+XOR Delay
Area of Memory Containing N Bits
Go Area of Memory Cell = (Area of One Bit Memory Cell*Absolute Frequency)/Array Efficiency
Area of Memory Cell
Go Area of One Bit Memory Cell = (Array Efficiency*Area of Memory Cell)/Absolute Frequency
Array Efficiency
Go Array Efficiency = (Area of One Bit Memory Cell*Absolute Frequency)/Area of Memory Cell
N-Input 'And' Gate
Go N-Input AND Gate = N-bit Carry Skip Adder/K-Input AND Gate
N-Bit Carry-Skip Adder
Go N-bit Carry Skip Adder = N-Input AND Gate*K-Input AND Gate
K-Input 'And' Gate
Go K-Input AND Gate = N-bit Carry Skip Adder/N-Input AND Gate

Tree Adder Delay Formula

Tree Adder Delay = Propagation Delay+log2(Absolute Frequency)*AND-OR Gate Delay+XOR Delay
ttree = tpg+log2(fabs)*Tao+Txor

What is tree adders?

For wide adders (roughly, N > 16 bits), the delay of carry-lookahead
(or carry-skip or carry-select) adders becomes dominated by the delay of passing the carry through the lookahead stages. This delay can be reduced by looking ahead across the lookahead blocks. In general, you can construct a multilevel tree of look-ahead structures to achieve delay that grows with log N. Such adders are variously referred to as tree adders, logarithmic adders, multilevel-lookahead adders, parallel-prefix adders, or simply lookahead adders.

How to Calculate Tree Adder Delay?

Tree Adder Delay calculator uses Tree Adder Delay = Propagation Delay+log2(Absolute Frequency)*AND-OR Gate Delay+XOR Delay to calculate the Tree Adder Delay, The Tree Adder Delay formula is defined as this comes at the cost of many long wires that must be routed between stages. The tree also contains more PG cells; while this may not impact the area if the adder layout is on a regular grid, it will increase power consumption. Despite these costs, the Kogge-Stone tree is widely used in high-performance 32-bit and 64-bit adders. In summary, a Sklansky or Kogge-Stone tree adder reduces the critical path. Tree Adder Delay is denoted by ttree symbol.

How to calculate Tree Adder Delay using this online calculator? To use this online calculator for Tree Adder Delay, enter Propagation Delay (tpg), Absolute Frequency (fabs), AND-OR Gate Delay (Tao) & XOR Delay (Txor) and hit the calculate button. Here is how the Tree Adder Delay calculation can be explained with given input values -> 1.6E+10 = 8.01E-09+log2(10)*2.05E-09+1.49E-09.

FAQ

What is Tree Adder Delay?
The Tree Adder Delay formula is defined as this comes at the cost of many long wires that must be routed between stages. The tree also contains more PG cells; while this may not impact the area if the adder layout is on a regular grid, it will increase power consumption. Despite these costs, the Kogge-Stone tree is widely used in high-performance 32-bit and 64-bit adders. In summary, a Sklansky or Kogge-Stone tree adder reduces the critical path and is represented as ttree = tpg+log2(fabs)*Tao+Txor or Tree Adder Delay = Propagation Delay+log2(Absolute Frequency)*AND-OR Gate Delay+XOR Delay. Propagation delay typically refers to the rise time or fall time in logic gates. This is the time it takes for a logic gate to change its output state based on a change in the input state, Absolute Frequency is the number of occurrences of a particular data point in a dataset. It represents the actual count or tally of how many times a specific value appears in the data, AND-OR Gate Delay in the gray cell is defined as the delay in the computing time in AND/OR gate when logic is passed through it & XOR Delay is the propagation delay of XOR gate.
How to calculate Tree Adder Delay?
The Tree Adder Delay formula is defined as this comes at the cost of many long wires that must be routed between stages. The tree also contains more PG cells; while this may not impact the area if the adder layout is on a regular grid, it will increase power consumption. Despite these costs, the Kogge-Stone tree is widely used in high-performance 32-bit and 64-bit adders. In summary, a Sklansky or Kogge-Stone tree adder reduces the critical path is calculated using Tree Adder Delay = Propagation Delay+log2(Absolute Frequency)*AND-OR Gate Delay+XOR Delay. To calculate Tree Adder Delay, you need Propagation Delay (tpg), Absolute Frequency (fabs), AND-OR Gate Delay (Tao) & XOR Delay (Txor). With our tool, you need to enter the respective value for Propagation Delay, Absolute Frequency, AND-OR Gate Delay & XOR Delay and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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