# Example of subtraction with borrow?

• posted

Could someone post a snippet of assembly language code showing how subtraction with borrow works? I am trying to do 12 bit math on a

4 bit processor, but any example such as doing 16 bit math on an 8 bit processor will do. I don't care which processor either; I am just trying to find an example of someone using the carry bit as a borrow bit so I can work things out in my mind. The addition with carry makes perfect sense, but I don't "get it" when it comes down to doing subtraction with borrowing. An example would help a lot.

Thanks!

• posted

From:

SUBB16_16: ;Step 1 of the process MOV A,R7 ;Move the low-byte into the accumulator CLR C ;Always clear carry before first subtraction SUBB A,R5 ;Subtract the second low-byte from the accumulator MOV R3,A ;Move the answer to the low-byte of the result

;Step 2 of the process MOV A,R6 ;Move the high-byte into the accumulator SUBB A,R4 ;Subtract the second high-byte from the accumulator MOV R2,A ;Move the answer to the low-byte of the result

;Return - answer now resides in R2, and R3. RET Calling sequence:

;Load the first value into R6 and R7 MOV R6,#22h MOV R7,#0DBh

;Load the first value into R4 and R5 MOV R4,#1Ah MOV R5,#0F9h

;Call the 16-bit subtraction routine LCALL SUBB16_16

• posted

Computers don't subtract (apart from the ones that don't add, anyway ;o).

Subtraction is performed by adding the negated value of the subtrahend, so: a - b == a + (-b)

To negate an integer (assuming a two's-complement representation), just invert all bits and add 1.

An example:

37 - 18 = 100101 - 010010 = 100101 + (101101 + 1) = 100101 + 101110 = 010011 = 19
• posted

Typically you set the "carry" bit for the first byte/nibble and then subtract. The carry is set low if there is a borrow.

multiple word subtraction in pseudo code:

sub: set carry ; if processor has no subtract without borrow load A0 ; minuend first word (least significant) subb B0 ; subtract subtrahend first word with borrow store R0 ; result first word (least significant) load A1 subb B1 store R0 ... load An subb Bn store rn ; result last word (most significant)

In fact, what's happening is that the processor is adding on the 1's complement of the subtrahend to the minuend, plus the carry.

eg. 4-bit nibble subtraction of 8 bit 0x0A (10) from 0x02 (2)

set carry load A0 ; 2 subb B0 ; add ~0xA = 5 + carry store R0 ; result is 8 with no carry (=> borrow) load A1 ; 0 subb B1 ; add ~0 = F (no carry) store R1 ; F (no carry)

Result: F8 = -8.

Best regards, Spehro Pefhany

• posted

and you implement that add 1 by having the carry set. For subtraction, that makes the carry bit a 'not borrow' bit for subtraction. Thus the only difference between subtraction and addition is the bit complement of the subtrahend, and either setting (subtract) or resetting (add) the carry for the very first of an extended add/subtract operation. I'm sure it is now crystal clear :-) but work out some examples for yourself.

This is fouled up where the chip designers have decided to invert it's purpose, as in the X86 processors.

• posted

The important thing is to realize that there are two different philosophies for setting the carry bit after subtraction.

Z80, x86, and SPARC treat the carry flag as a "borrow flag" when doing a subtraction. If the subtrahend is greater than the minuend (treating both operands as unsigned), the carry flag is set because there is a borrow. A "branch if less unsigned" after a comparison instruction is equivalent to "branch if carry set" in this case.

On other processor families, such as ARM and PowerPC, the carry flag after a subtraction is set to the adder carry output after computing (~b + a + 1). Therefore, if the subtrahend is less or equal to the minuend (treating both operands as unsigned), the carry flag is set. "branch if less unsigned" after a comparison instruction is equal to "branch if carry clear" in this case.

-- Norbert

• posted

And that's only on two's-complement machines. The old Univac 1100 series mainframes used one's-complement coding (so it had +0 and -0), and a hardware subtractor that required an "end-around-borrow"!

• posted

And no carry status. Multi-precision arithmetic required some real coding gymnastics!

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