Signed and Unsigned Numbers

http://www.electronics.dit.ie/staff/tscarff/signed_numbers/signed_numbers.htm

http://stackoverflow.com/questions/9939760/how-do-i-convert-an-integer-to-binary-in-javascript

http://stackoverflow.com/questions/16155592/negative-numbers-to-binary-string-in-javascript

3down vote

Short answer:

1. The toString() function basically takes the decimal, converts it to binary and adds a "-" sign.
2. A zero fill right shift converts it's operand to a 32 signed bit integer in two complements format.

A more detailed answer:

Question 1:

//If you try
(-3).toString(2); //show "-11"

It's in the function .toString(). When you output a number via .toString():

Syntax

numObj.toString([radix])

If the numObj is negative, the sign is preserved. This is the case even if the radix is 2; the string returned is the positive binary representation of the numObj preceded by a - sign, not the two's complement of the numObj.

So basically it takes the decimal, converts it to binary and adds a "-" sign. 

1. Base 10 "3" converted to base 2 is "11"
2. Add a sign gives us "-11"

Question 2:

// but if you fake a bit shift operation it works as expected
        (-3 >>> 0).toString(2); // print "11111111111111111111111111111101"

A zero fill right shift converts it's operand to a 32 signed bit integer.

The operands of all bitwise operators are converted to signed 32-bit integers in two's complement format.

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answered Jun 7 '16 at 15:11 Daan 2,29421936

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An 8 bit number system can be used to create 256 combinations (from 0 to 255),  and the first 128 combinations (0 to 127)  represent positive numbers and next 128 combinations (128 to 255)  represent negative numbers.

unsigned 0~256

singed   0 ~ +127  &  -1 ~ -128

> -3>>>0

4294967293

> 

shift的功能在於往右移並在前面補零

而>>>後面代表的是要移多少格

這邊-3移了零格但作為singed的符號1卻被轉為數字1，意義上有所不同

放在二進位中 -3 跟 4294967293 兩者是相等的

順帶一提要得到 -3 也可以用二補數的方式
以八位元為例
0000 0011 (3)
將3的二進位反相得到3的補數
1111 1100
三的補數再加一得到二補數 (規則是加上補數-1，可複習singed number系統)
1111 1101 (-3)