Question 33.2: Rent ’ s Rule The 18-mm square chips in Example 33.1 are mi...
Rent ’ s Rule
The 18-mm square chips in Example 33.1 are microprocessors with a processable area of 17 mm by 17 mm. The density of circuits within each chip ’ s processable area is 500 circuits per mm² . Determine the number of (a) internal circuits that can be placed on each chip and (b) input/output terminals that would be required in the packaged microprocessor using Rent ’ s rule. (c) If the packaged IC were a static random access memory device instead of a microprocessor, how many input/output terminals would be required? Refer to Table 33.4 for appropriate values of the parameters in Rent ’ s rule.
| Integrated Circuit Type and Concise Definition{}^a | Typical values{}^b | |
| Constant C | Exponent m | |
| Microprocessor. An IC that functions as the central processing unit (CPU) of a computer. It is programmable and operates on instructions stored in internal memory to process digital data input and provide digital output. | 0.89 | 0.45 |
| Gate array. A partially completed IC in which transistors and other devices are located at predefined locations so they can be interconnected by means of one or more final layering processes to provide specific functionality to the IC. Also known as an uncommitted logic array. | 1.9 | 0.5 |
| Static random access memory (SRAM). An IC memory device that stores data bits as long as power is supplied. It does not need to be periodically refreshed as in dynamic random access memory. | 6.9 | 0.12 |
| Dynamic random access memory (DRAM). An IC memory device that uses capacitors to store data. The capacitors require periodic recharging; hence the term dynamic. DRAM is a slower but less expensive data-storage device compared to SRAM. | 7.8 | 0.07 |
(a) The processable area of each chip = (17)² = 289 mm²
Number of internal circuits n_{ic}= 289 (500) = 144,500
(b) From Table 33.4 , C = 0.89 and m = 0.45 :
n_{io}=Cn_{ic}^m=0.98(144,500)^{0.45}= 187 input output terminals
(c) From Table 33.4 , C = 6.9 and m = 0.12 :
n_{io}=Cn_{ic}^m=6.9(144,500)^{0.12}= 29 input output terminals
Table 33.4
| Integrated Circuit Type and Concise Definition{}^a | Typical values{}^b | |
| Constant C | Exponent m | |
| Microprocessor. An IC that functions as the central processing unit (CPU) of a computer. It is programmable and operates on instructions stored in internal memory to process digital data input and provide digital output. | 0.89 | 0.45 |
| Gate array. A partially completed IC in which transistors and other devices are located at predefined locations so they can be interconnected by means of one or more final layering processes to provide specific functionality to the IC. Also known as an uncommitted logic array. | 1.9 | 0.5 |
| Static random access memory (SRAM). An IC memory device that stores data bits as long as power is supplied. It does not need to be periodically refreshed as in dynamic random access memory. | 6.9 | 0.12 |
| Dynamic random access memory (DRAM). An IC memory device that uses capacitors to store data. The capacitors require periodic recharging; hence the term dynamic. DRAM is a slower but less expensive data-storage device compared to SRAM. | 7.8 | 0.07 |