Area Analysis I : Natural Ratio vs. Square Ratio

Basic Assumption

(1) Technology : 0.35um CMOS process
(2) Operating Voltage : 2.5 V
(3) Operating Temperature : 25 C
(4) Circuit : Dual-Rail Domino Logic
(5) 16 bit Multiplier : The radix-4 Booth Algorithm

Area Estimation Method

(1) The Area calculation is based on the paper, Carl Lemonds, "A High Throughput 16 by 16 Bit Multiplier for DSP Cores", IEEE International Symposium on Circuits and Systems, 1996. p479.
(2) Transformation of Area Calculation in Table III of the paper, Carl Lemonds

[ TABLE 19 ]

(3) Area Estimation for Sail Boat

Number of Transistors in 4 bit Register
8 2inputMux : 8 * 4 = 32 transistors
33 inverter : 33 * 2 = 66 transistors
Total : 98 transistors

Number of Transistors in 16 bit Register
98 * 4 = 392 transistors

Number of Transistors in 16 bit Mux
16 * 4 = 64 transistors

Components of Sail Boat : Square Ratio
Total Number of 16bit Mux : 88 16bitMux
88 * 64 = 5632 transistors
Registers : 48 Registers
48 * 392 = 18816 transistors

Area Calculation for Sail Boat : Square Ratio
5632 * 1.832 uW + 18816 * 7.462 um = 150.72 mm

Components of Sail Boat : Natural Ratio (16bit)
Total Number of 16bit Mux : 39 16bitMux
39 * 64 = 2496 transistors
Registers : 34 Registers
34 * 392 = 13328 transistors

Area Calculation for Sail Boat : Natural Ratio
2496 * 1.832 um + 13328 * 7.462 um = 104.03 mm

(4) Area Estimation for 16 bit Multiplier

4 16bit multiplier : 4 * 111,064 um = 444.26 mm (5) 48 bit Wallace Tree

3to2 Wallace Tree Compressor has 30 transistors.
2to2 Wallace Tree Compressor has 14 transistors.
5to3 Wallace Tree Compressor has 52 transistors.

48 bit Wallace Tree has 48 3to2 Wallace Tree Compressors,
45 2to2 Wallace Tree Compressors,
17 5to3 Wallace Tree Compressors.
Total number of transistors is 48*30 + 45*14 + 17*52 = 2954.
Area : 2954 * 5.217 um = 15.41 mm

Four 48 bit Wallace Tree = 61.64 mm
(6) 96 bit Wallace Tree

96 bit Wallace Tree has 95 3to2 Wallace Tree Compressors,
92 2to2 Wallace Tree Compressors,
33 5to3 Wallace Tree Compressors.
Total number of transistors is 95*30 + 92*14 + 33*52 = 5854.
Channel Width: 5854 * 5.217 um = 30.54 mm

(7) 48 bit Adder

Channel Width : 38.74 mm

Four 48 bit Adders : 4 * 38.736 mm = 154.94 mm
(8) 96 bit Adder

Channel Width : 98.957 mm

(9) 32 bit FP converter

Area ~ 32 bit Adder's Area with half adder
= 22.379 * (14/30) = 10.44 mm

Four 32 bit FP converter : 41.77 mm (10) 64 bit FP converter

Area ~ 64 bit Adder's Area consumption with half adder
= 57.170 * (14/30) = 26.68 mm

(11) Output Registers

32bit Registers: 784 transistors
16bit Registers: 392 transistors

Natural Ratio

2 * 4 * 392 * 7.462 um = 23.40 mm

Square Ratio

2 * 16 * 392 * 7.462 um = 93.60 mm

(12) Area Table 20 : Natural Ratio vs. Square Ratio

[ TABLE 20 ]