Menu
The main use of 1's complement is to represent a signed binary number. Apart from this, it is also used to perform various arithmetic operations such as addition and subtraction. In signed binary number representation, we can represent both positive and negative numbers.
Unisys 1100/2200 legacy systems use 1's complement arithmetic, and this continues in the newer Dorado series.
A ones' complement system or ones' complement arithmetic is a system in which negative numbers are represented by the inverse of the binary representations of their corresponding positive numbers.
While in 1's complement is not used for negative integers however it can be used with arithmetic operation of natural numbers so we prefer 2's complement over 1's complement. Two's complement allows negative and positive numbers to be added together without any special logic.
I work in the telemetry field and we have some of our customers have old analog-to-digital converters that still use 1's complement. I just had to write code the other day to convert from 1's complement to 2's complement in order to compensate.
So yes, it's still out there (but you're not going to run into it very often).
This all comes down to knowing your roots.
Yes, this is technically an old technique and I would probably do what other people suggested in that question and use the modulo (%) operator to determine odd or even.
But understanding what a 1s complement (or 2s complement) is always a good thing to know. Whether or not you ever use them, your CPU is dealing with those things all of the time. So it can never hurt to understand the concept. Now, modern systems make it so you generally never have to worry about things like that so it has become a topic for Programming 101 courses in a way. But you have to remember that some people actually would still use this in the "real world"... for example, contrary to popular belief there are people who still use assembly! Not many, but until CPUs can understand raw C# and Java, someone is going to still have to understand this stuff.
And heck, you never know when you might find your self doing something where you actually need to perform binary math and that 1s complement could come in handy.
The CDC Cyber 18 I used back in the '80 was a 1s complement machine, but that's nearly 30 years ago, and I haven't seen one since (however, that was also the last time I worked on a non-PC)
RFC 791 p.14 defines the IP header checksum as:
The checksum field is the 16 bit one's complement of the one's complement sum of all 16 bit words in the header. For purposes of computing the checksum, the value of the checksum field is zero.
So one's complement is still heavily used in the real world, in every single IP packet that is sent. :)
I've never encountered a one's complement system, and I've been coding as long as you have.
But I did encounter a 9's complement system -- the machine language of a HP-41c calculator. I'll admit that this can be considered obsolete, and I don't think they ever had a C compiler for those.
I decided to find one. The Unisys ClearPath systems have an ANSI C compiler (yes they call it "American National Standard C" for which even the PDF documentation was last updated in 2013. The documentation is available online;
There the signed types are all using one's complement representation, with the following properties:
Type | Bits | Range
---------------------+------+-----------------
signed char | 9 | -2⁸+1 ... 2⁸-1
signed short | 18 | -2¹⁷+1 ... 2¹⁷-1
signed int | 36 | -2³⁵+1 ... 2³⁵-1
signed long int | 36 | -2³⁵+1 ... 2³⁵-1
signed long long int | 72 | -2⁷¹+1 ... 2⁷¹-1
Remarkably, it also by default supports non-conforming unsigned int and unsigned long, which range from 0 ... 2³⁶ - 2, but can be changed to 0 ... 2³⁶ - 1 with a pragma.
If you love us? You can donate to us via Paypal or buy me a coffee so we can maintain and grow! Thank you!
Donate Us With