Bitmask tables

At $WORK I have a need to create some bitmasks over a 64-bit field. I've never done this before. I figured that surely tables exist for grabbing a certain number of bits from a certain position, but I never found those tables. So, to scratch my own itch I wrote a very simple Python program to generate the tables and used a CSV to Markdown converter to create the tables. Here you go, now we both have a quick reference. Update 2023-04-04: Someone on Mastodon mentioned bitwise, an interactive terminal program for bit manipulations. It looks pretty cool! ## ProgramSVG Image python bit_sizes = [1, 8, 16, 32] total_bits = 64 for bit_size in bit_sizes: positions = int(total_bits / bit_size) n = 0 for _ in range(bit_size): n = n << 1 n += 1 print(f"# {bit_size} bits") for pos in range(positions): print(f"{pos}, {n}") n = n << bit_size ## Table formatSVG Image Each table has a "position" column and a "decimal value" column. The "position" refers to which n bits you're setting to 1. For a single bit the position is which individual bit is 1. For 8 bits the position is which 8 bits you're setting to 1. The decimal value is the decimal value when the bits at the given position are set to 1. For example, 8 bits in position 1 (the second byte) corresponds to the binary number 0b000....01111111100000000 and the decimal value 65280. To get the mask for an odd number of bits you can just add the decimal values in the table since the positions don't overlap for a given number of bits. ## 1 bitSVG Image | Position | Decimal Value | | -------- | ------------------- | | 0 | 1 | | 1 | 2 | | 2 | 4 | | 3 | 8 | | 4 | 16 | | 5 | 32 | | 6 | 64 | | 7 | 128 | | 8 | 256 | | 9 | 512 | | 10 | 1024 | | 11 | 2048 | | 12 | 4096 | | 13 | 8192 | | 14 | 16384 | | 15 | 32768 | | 16 | 65536 | | 17 | 131072 | | 18 | 262144 | | 19 | 524288 | | 20 | 1048576 | | 21 | 2097152 | | 22 | 4194304 | | 23 | 8388608 | | 24 | 16777216 | | 25 | 33554432 | | 26 | 67108864 | | 27 | 134217728 | | 28 | 268435456 | | 29 | 536870912 | | 30 | 1073741824 | | 31 | 2147483648 | | 32 | 4294967296 | | 33 | 8589934592 | | 34 | 17179869184 | | 35 | 34359738368 | | 36 | 68719476736 | | 37 | 137438953472 | | 38 | 274877906944 | | 39 | 549755813888 | | 40 | 1099511627776 | | 41 | 2199023255552 | | 42 | 4398046511104 | | 43 | 8796093022208 | | 44 | 17592186044416 | | 45 | 35184372088832 | | 46 | 70368744177664 | | 47 | 140737488355328 | | 48 | 281474976710656 | | 49 | 562949953421312 | | 50 | 1125899906842624 | | 51 | 2251799813685248 | | 52 | 4503599627370496 | | 53 | 9007199254740992 | | 54 | 18014398509481984 | | 55 | 36028797018963968 | | 56 | 72057594037927936 | | 57 | 144115188075855872 | | 58 | 288230376151711744 | | 59 | 576460752303423488 | | 60 | 1152921504606846976 | | 61 | 2305843009213693952 | | 62 | 4611686018427387904 | | 63 | 9223372036854775808 | ## 8 BitsSVG Image | Position | Decimal Value | | -------- | -------------------- | | 0 | 255 | | 1 | 65280 | | 2 | 16711680 | | 3 | 4278190080 | | 4 | 1095216660480 | | 5 | 280375465082880 | | 6 | 71776119061217280 | | 7 | 18374686479671623680 | ## 16 bitsSVG Image | Position | Decimal Value | | -------- | -------------------- | | 0 | 65535 | | 1 | 4294901760 | | 2 | 281470681743360 | | 3 | 18446462598732840960 | ## 32 bitsSVG Image | Position | Decimal Value | | -------- | -------------------- | | 0 | 4294967295 | | 1 | 18446744069414584320 |