Embedded 1 - Computer Arithmetic and Logic Basics

Unsigned Binary Integers

Range: 0 to +2^n - 1

ex) Use 32-bits --> 0 to +4,294,967,295

Signed Binary Integers

Range: -2^n-1 to +2^n-1 - 1

ex) 32-bits --> -2,147,483,648 to +2,147,483,647

MSB is signed bit

overflow - signed numbers

adding + and - = no overflow

adding two + operands = overflow if result N=1 (looks neg but is pos)

adding two - operands = overflow if N=0 (looks pos)

S Suffix in ARM instructions

modifies the condition flags of CSPR

What would you observe for 8-bit operations? Are flags updated correctly?

flags are 32-bit based, must sign extend for it to work as expected

Sign Extension

takes MSB bit in the byte or half word and duplicates it up to the full data width

Positive number looks negative

there is carry from 30 to 31 but no carry put of 31 (C=0) --> N=1, V=1, C=0

Negative number looks positive

there is carry out of 31 (C=1) but no carry from 30 to 31 --> N=0, V=1, C=1

multiplication of signed numbers

mul Rd,Rn,Op2 // Rd = Rn*Op2

umull RdLo,RdHi,Rn,Rm

smull Rdlo,Rdhi,Rm,Rn

division

udiv Rd, Rm, Rn Rd = Rm / Rn [unsigned - only does integer division]

sdiv Rd,Rm,Rn Rd = Rm / Rn [signed]

conditional execution

Movxx

xx = EQ, NE, LT, GT, GE, LE

- condition is based on prior instruction that changed the flags

CMP

same as SUBS except result is discarded, flags are set

--> CMP RN, OP2 (RN-OP2)

CMN

same as ADDS except result discarded, flags set --> CMN RN, Op2 (RN + Op2)

LSL instruction

bits are shifted from R to L, 0 enters LSB and MSB exits to carry flag

MOVS Rd, Rn, LSL #numOfShiftLSL(S) Rd, Rn, #numOfShift

LSR instruction

bits are shifted from L to R, 0 enters MSB and LSB exits to carry flag

LSR(S) Rd, Rn, #numOfShift ;Logical Shift RightMOVS Rd, Rn, LSR #numOfShift

ROR instruction

bits roatetd from L to R, LSB goes to MSB and to the carry flag

ROR Rd, Rm, #numOfShifts ;Rotate Rm right Rn bit positions

MOVS Rd, Rm, ROR #numOfShifts

RRXS instruction

RRXS the C is moved to the MSB, and the LSB is moved to the C

ASR Instruction

MSB is held constant and the LSB exits to

the carry flag

ASR(S) Rd, Rm, #count @Arithmetic Shift Right

MOVS Rd, Rm, ASR #count

Preserves the sign!

What can AND be used for?

to clear specific bits of a byte

What can OR be used for?

to set specific bits of a byte