Redundant binary signed-digit

[gilianzz]

Hello everyone!

Today I present to you....the redundant binary signed-digit number system.

What is redundant binary?

A redundant binary representation (RBR) is a numeral system that uses more bits than needed to represent a single binary digit so that most numbers have several representations.

What's the signed-digit thingy?

When digits have signs, that RBR is also a signed-digit representation.
RBSD (redundant binary signed digit) uses 2 bits for 1 digit.
00=-1
01=0
10=0
11=1

What are the advantages of RBSD?

-No need for 2's complement, to negate you just invert all bits and you can represent all positive and negative numbers.
00->11 (-1->1)
01->10 (0->0)
10->01 (0->0)
11->00 (1->-1)
-Addition is carryless!
this means that there will be a constant delay no mather what bitsize you are using, 8 bits=4585346969 bits.

What are the disadvantages of RBSD?
-2 bits for 1 digit
-conversions from RBSD to 2's complement

How to make an RBSD adder?

http://en.wikipedia.org/wiki/Redundant_b...esentation

I made an adder in minecraft for it but I suck at making stuff fast, maybe you guys can improve it

[greatgamer34]

this is quite interesting, although I recommend you look up nega bases, such as; nega-decimal and nega-binary.

they basically make negatives super easy.
http://en.wikipedia.org/wiki/Negative_base

[Cutlassw30]

niga-binary




XXX420BASSSWAGXXXXLIVINGITUPXXYOUKNOWITBABYxxxx69foooooooooooooooools

[greatgamer34]

niga-binary




XXX420BASSSWAGXXXXLIVINGITUPXXYOUKNOWITBABYxxxx69foooooooooooooooools

not quite.. lmfao.

a nega-binary adder would be really tough to implement.

I cant wait for gilianzz to show me this on the server!

[gilianzz]

this is quite interesting, although I recommend you look up nega bases, such as; nega-decimal and nega-binary.

they basically make negatives super easy.
http://en.wikipedia.org/wiki/Negative_base

I've made a negabinary adder on minecraft aswell, unfortunately they are quite slow and bulky, and the amount of positive vs negative numbers is not symmetrical, for example with 4 bits you have a range of -10,5

[greatgamer34]

Can you set a warp to your adder for me? I really want to check it out when i get home!

[gilianzz]

Can you set a warp to your adder for me? I really want to check it out when i get home!

/warp gilian
for the RBSD adder, remember what 00,01,10,11 means
for the negabinary, it was on the previous server but i'm trying to remake it, the logic is very bulky though

[greatgamer34]

1 0 0 1

[gilianzz]

I made a 4 bit negabinary adder next to it aswell, it's slow and huge.

[jxu]

The adder design you posted is basically the concept of a carry save adder (I think)

[EDevil]

Did someone mention CARRY SAVE ADDER?

http://forum.openredstone.org/showthread.php?tid=1402

[gilianzz]

The adder design you posted is basically the concept of a carry save adder (I think)

Yes it's a kind of carry save adder, but this also uses another number system instead of ordinary binary.