LFSR伪随机数产生多项式 – EnChip Microelectronics

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By zhagangPosted on 2023-10-20Posted in 未分类Tagged Design

LFSR = Linear-feedback shift register
Reference: https://en.wikipedia.org/wiki/Linear-feedback_shift_register

Bits (n)	Feedback polynomial	Taps	Taps (hex)	Period ( $2^{n}-1$ )
2	$x^{2}+x+1$	11	0x3	3
3	$x^{3}+x^{2}+1$	110	0x6	7
4	$x^{4}+x^{3}+1$	1100	0xC	15
5	$x^{{5}}+x^{{3}}+1$	10100	0x14	31
6	$x^{{6}}+x^{{5}}+1$	110000	0x30	63
7	$x^{{7}}+x^{{6}}+1$	1100000	0x60	127
8	$x^{{8}}+x^{{6}}+x^{{5}}+x^{{4}}+1$	10111000	0xB8	255
9	$x^{{9}}+x^{{5}}+1$	100010000	0x110	511
10	$x^{{10}}+x^{{7}}+1$	1001000000	0x240	1,023
11	$x^{{11}}+x^{{9}}+1$	10100000000	0x500	2,047
12	$x^{{12}}+x^{{11}}+x^{{10}}+x^{{4}}+1$	111000001000	0xE08	4,095
13	$x^{{13}}+x^{{12}}+x^{{11}}+x^{{8}}+1$	1110010000000	0x1C80	8,191
14	$x^{{14}}+x^{{13}}+x^{{12}}+x^{{2}}+1$	11100000000010	0x3802	16,383
15	$x^{{15}}+x^{{14}}+1$	110000000000000	0x6000	32,767
16	$x^{16}+x^{15}+x^{13}+x^{4}+1$	1101000000001000	0xD008	65,535
17	$x^{{17}}+x^{{14}}+1$	10010000000000000	0x12000	131,071
18	$x^{{18}}+x^{{11}}+1$	100000010000000000	0x20400	262,143
19	$x^{{19}}+x^{{18}}+x^{{17}}+x^{{14}}+1$	1110010000000000000	0x72000	524,287
20	$x^{20}+x^{17}+1$	10010000000000000000	0x90000	1,048,575
21	$x^{21}+x^{19}+1$	101000000000000000000	0x140000	2,097,151
22	$x^{22}+x^{21}+1$	1100000000000000000000	0x300000	4,194,303
23	$x^{23}+x^{18}+1$	10000100000000000000000	0x420000	8,388,607
24	$x^{24}+x^{23}+x^{22}+x^{17}+1$	111000010000000000000000	0xE10000	16,777,215

LFSR伪随机数产生多项式