# 1 bit Full Subtractor

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i am really confused on how to construct a truth table for a one b!t Fu11 Subtr4ct0r
....everywhere i've looked, i see them using 3 inputs(borrow in,input A,input B) and for output there is 2(sum bit,borrow out). I dont understand the borrow out bit. I know if u subtract bit 0-1 you cannot and must perform a borrow in from the bit in front of it. but What the heck is a borrow out used for in subtraction? if anyone could give a binary subtraction example + decimal subtraction example showing how borrowin and borrow outs are both used id be greatly appreciated.

-thx

[Edited by - Sneftel on October 25, 2010 12:26:15 PM]

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Borrow out is how the Nth bit tells the N+1th bit "I'm borrowing from you". Borrow in is how the Nth bit finds out from the N-1th bit "I borrowed from you". It's very similar to the carry bit in the full adder.

Bit3 Bit2 Bit1 Bit0
1 1 0 0
- 0 0 0 1
------------------
1 0 1 1

Bit0 has to subtract 1, but only has a 0 to subtract from. He sets borrow-out to 1, (his borrow-in is 0, since he's the lowest bit), meaning he's borrowing a 2, and 2-1=1. Bit1 was going to subtract 0-0 and get 0, but now his borrow-in is 1 (because it's connected to Bit0's borrow-out), so now he has 0-0-1, which again can't be done. So he also borrows 2, this time from Bit2, by setting borrow-out, and thus performs (2+0)-0-1=1. Bit2 gets the borrow-in from Bit1, and does 1-0-1=0; he doesn't have to borrow, so his borrow-out is 0. Bit3 doesn't have borrow-in set, so he just does 1-0=1.

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