Q:

SN74HC595N Seems to misread bits

A prenote; I'm not sure if this falls more into electronics or Arduino, but I think Shift Registers are more so electronic and binary related.  
I'm using a single SN74HC595N shift register connected to my Arduino Uno. I'm using Arduino's shiftOut function, but when I send a byte, for example, 11111111, Only Output1 and Output7 are active. I also tried a few different ones, such as01010101 and still, the output seemed nothing like what I would expect (Except 00000000 which did as I expected, and turned all the LEDs off). Here is a chart of the connections to the Arduino:   

~the output pins are connected to 3mm LED's through resistors; Everything is directly wired, but VCC is demodulated with two 0.1uF, and a 10uF capacitor, that connects to GND to filter any high frequencies and smooth out the input  
And my simple code: 
int latchPin = 12;
int clockPin = 11;
int dataPin = 13;

void setup(){
    pinMode(latchPin, OUTPUT);
    pinMode(dataPin, OUTPUT);
    pinMode(clockPin, OUTPUT);

    digitalWrite(latchPin, LOW);
    digitalWrite(clockPin, LOW);
    shiftOut(dataPin, clockPin, LSBFIRST, 1111111);
    digitalWrite(latchPin, HIGH);
    digitalWrite(clockPin, HIGH);

}

void loop(){

}

I am brand new to shift registers (and unfamiliar with bytes) so I apologize for any incompetence, and thank you for the help! 
EDIT:
Now, when I send 11111111, I get pins 0, 1, 2, 3, and 7 to turn on. I confirmed this with my multimeter, the active pins read 4.85 volts, whereas the deactivated pins read 0 volts. 

A:

You need to provide a byte (uint8_t) for the data to be shifted out. Your 11111111 is being interpreted as a decimal literal so you're getting some part of that. I would expect the number 11111111 = 0xA98AC7 to come out as 0xC7 , which does not exactly match  what you are seeing- so perhaps there is something else wrong in addition. 
Try shiftOut(dataPin, clockPin, LSBFIRST, 0xFF); for all on. 
If you prefer binary to hex, you should be able to use 0b11111111 .. that binary format is supported by GCC and thus Ardunio. 

