3.3. Masking¶

Masking is the process of using bitwise operations to isolate part of a binary pattern. As an example, here are the bits that represent the ARM machine code for ADD r1, r2, r3. Bits 12-15 have the destination register:

31	30	29	28	27	26	25	24	23	22	21	20	19	18	17	16	15	14	13	12	11	10	9	8	7	6	5	4	3	2	1	0
1	1	1	0	0	0	0	0	1	0	0	0	0	0	1	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	1	1
E				0				8				2				1				0				0				3

To isolate that register from the pattern, we could AND with 0xF000 (hex for 1111 0000 0000 0000):

31	30	29	28	27	26	25	24	23	22	21	20	19	18	17	16	15	14	13	12	11	10	9	8	7	6	5	4	3	2	1	0
0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	1	1	0	0	0	0	0	0	0	0	0	0	0	0
0				0				0				0				F				0				0				0

The bits that were ANDed with 1, will retain their value. The bits that were ANDed with 0, are forced to 0:

31	30	29	28	27	26	25	24	23	22	21	20	19	18	17	16	15	14	13	12	11	10	9	8	7	6	5	4	3	2	1	0
0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0
0				0				0				0				1				0				0				0

Recall that immediates can generally be no more than two consecutive hex chars padded with 0s (like 0xFF or 0xA4000 but not 0xF00F where the two non-zero chars are spaced out). Those patterns can be masked directly with an AND. Larger patterns must be built up in a register before being used as a mask:

LDR   r5, =0x1BADDEED

@isolate bits 0-7 (last byte: 0xED)
@ & means bitwise OR
AND   r6, r5, #0xFF        @r6 = 0x1BADDEED & 0x000000FF = 0x000000ED


@isolate bits 8-15 (next to last byte: 0xDE)
AND   r7, r5, #0xFF00      @r7 = 0x1BADDEED & 0x0000FF00 = 0x0000DE00


@isolate bits 16-27 (0xBAD from 0x1BADDEED)
@ want pattern 0x0FFF0000, but that takes too many bits to represent, so build it
MOV   r8, #0x00FF0000      @Start with 00FF0000
ORR   r8, r8, #0x0F000000  @r8 = 00FF0000 | 0F000000 = 0FFF0000
AND   r8, r5, r8           @r8 = 0x1BADDEED & 0x0FFF0000 = 0x0BAD0000

@isolate bits 2-5 :
@Use mask         0000 ... 0011 1100 = 3C
@r5 has           ???? ... 1110 1101 (...ED)
@   result ==     0000 ... 0010 1100 = 0x2C
AND   r8, r5, #0x3C        @r8 = 0x1BADDEED & 0x0000003C = 0x0000002C

end:  b end       @stop program

Try sample

A mask leaves the bits in their original location. If we want to use the masked value as a number, we would have to shift its bits so the leftmost one is aligned with the 0 bit.

If our goal is to end with the desired bits aligned to the right of the register, it may be simpler to just use a pair of shifts to clear extra bits and align the ones we want with bit 0. As an example, we will isolate bits 12-15 in the pattern below and align them with bit 0:

31	30	29	28	27	26	25	24	23	22	21	20	19	18	17	16	15	14	13	12	11	10	9	8	7	6	5	4	3	2	1	0
1	1	1	0	0	0	0	0	1	0	0	0	0	0	1	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	1	1
E				0				8				2				1				0				0				3

First we need to clear out everything past bit 15. We can do this by left shifting by 16 bits:

31	30	29	28	27	26	25	24	23	22	21	20	19	18	17	16	15	14	13	12	11	10	9	8	7	6	5	4	3	2	1	0
0	0	0	1	0	0	0	0	0	0	0	0	0	0	1	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
1				0				0				3				0				0				0				0

Then, we shift back to the right. There are 32 total bits, and we want to preserve just 4. So shift right 28 bits:

31	30	29	28	27	26	25	24	23	22	21	20	19	18	17	16	15	14	13	12	11	10	9	8	7	6	5	4	3	2	1	0
0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1
0				0				0				0				0				0				0				1

LDR   r5, =0xE0821003

@isolate bits 12-15 using just shifts
LSL   r9, r5, #16          @r9 = 0x10030000
LSR   r9, r9, #28          @r9 = 0x00000001

LDR   r6, =0x1BADDEED
@isolate bits 16-27 (0xBAD from 0x1BADDEED) using just shifts
LSL   r10, r6, #4          @r10 = 0xBADDEED0
LSR   r10, r10, #20        @r10 = 0x00000BAD

Try sample

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