Start New Discussion within our **Software Development Community** Answered # Convert negative decimal to binary

davidjhay jai.mahadeokar Pierre Maurette jrcagle 77 jrcagle 77 Featured Reply Jason43 klickagent

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Working with negative numbers in binary you need to use twos complement method. It is a bit confusing to start with (well it was for me). I use it a lot for checksum calculations. Hope this helps.

http://www.rsu.edu/faculty/PMacpherson/Programs/twos.html

David

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you can try Ex-Or ing the positive number with 10000000... it will work for numbers less than 01111111

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Hi, I'm having trouble trying to figure out a code that converts negative decimal numbers to binary, as well as specifying the number of bits. For example. convert -18 using 8 bits. This should come out as 10010010 doing it manually, I think. I'd appreciate the help, thanks.

Hum... 10010010 is a bit-sign representation (sign bit followed by the 7 bit representation of 18) wich is very unusual. If you want the complement to 2 reprrésentation, you have to know that whith 8 bits, the binary for N negative is the same than the positive for 255 + N + 1, 238 for -18. I assume you know how to convert a positive value to binary. Look at this, I think it works for any BITS value:

```
BITS = 8
MAXFORBITS = 1
for i in range (0,BITS):MAXFORBITS *= 2
print MAXFORBITS
testvaleur = -18
print (MAXFORBITS + testvaleur) % MAXFORBITS
testvaleur = 18
print (MAXFORBITS + testvaleur) % MAXFORBITS
```

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So in the manual, it says

Of course, Python doesn't use 8-bit numbers. It USED to use however many bits were native to your machine, but since that was non-portable, it has recently switched to using an INFINITE number of bits. Thus the number -5 is treated by bitwise operators as if it were written "...1111111111111111111010".

How?! Specifically, how do they do this efficiently?

Jeff

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Oh, nevermind. I thought it was saying something else. All it's saying is that when it performs right-shifts, it rolls in the MSB from the left. (Arithmetic instead of Logical shift)

I thought it was saying that it somehow represented negatives as if they had infinite precision, which would be impressive.

Jeff

1

Hi, I'm having trouble trying to figure out a code that converts negative decimal numbers to binary, as well as specifying the number of bits. For example. convert -18 using 8 bits. This should come out as 10010010 doing it manually, I think. I'd appreciate the help, thanks.

This may help you out:

Signed Numbers (2 methods)

Signed‐and‐Magnitude

Leading digit is the sign: 0 = positive; 1 = negative

+9 = 00001001

-9 = 10001001

+23 = 00010111

-23 = 10010111

2’s Compliment

Decimal to Binary

Invert all 0’s and 1’s, and add 1.

+9 = 00001001

-9 = 11110110

00000001 +

--------

11110111

+23 = 00010111

-23 = 11101000

00000001 +

--------

11101001

Binary to Decimal

Check the sign bit. If the sign bit is 0, number is positive, and you’re done. If it is 1, then number is negative, so invert

the bits and add 1.

00001101 = positive number

= + 13 (Done)

11110010 negative number

00001100 invert

00000001 + add one

--------

00001101 = - 13

11111111 negative number

00000000 invert

00000001 + add one

--------

00000001 = - 1

10000000 negative number

01111111 invert

00000001 + add one

--------

10000000 = - 128

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to convert signed binary to decimal you can use: convert signed binary to decimal or decimal to signed binary (any precision)

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