Hold ⌘-R during startup until you see a window similar to this:

These are your options:

1. Choose Utilities>Terminal:

Your OS X disk will be mounted in /Volumes/<your disk name>. For example, on my Mac it was mounted in /Volumes/Mavericks:

    df
    Filesystem     1K-blocks      Used Available Use% Mounted on
    /dev/disk0s2   249219484 145891460 103072024  59% /Volumes/Mavericks

Now copy /bin to your OS X disk:

    cp -a /bin /Volumes/<your disk name>

Note that the contents of /bin will be outdated, as the recovery disk is not updated with the rest of the OS, so restore /bin from Time Machine after successfully starting your Mac and logging in.

2. If you have a recent backup, choose "Restore From Time Machine Backup" and restore your Mac. Note that you will loose any changes you made after that backup.

Good luck.

If you are sure your Recovery HD is patched to match the OS on your main system, you can snag a file and see if it works without needing to do a full reinstall of the OS.

Hold ⌘-R during startup until you see a window similar to this:

These are your options:

1. Choose Utilities>Terminal:

Your OS X disk will be mounted in /Volumes/<your disk name>. For example, on my Mac it was mounted in /Volumes/Mavericks:

    df
    Filesystem     1K-blocks      Used Available Use% Mounted on
    /dev/disk0s2   249219484 145891460 103072024  59% /Volumes/Mavericks

Now copy /bin to your OS X disk:

    cp -a /bin /Volumes/<your disk name>

Note that the contents of /bin will be outdated, as the recovery disk is not updated with the rest of the OS, so restore /bin from Time Machine after successfully starting your Mac and logging in.

Hold ⌘-R during startup until you see a window similar to this:

These are your options:

1. Choose Utilities>Terminal:

Your OS X disk will be mounted in /Volumes/<your disk name>. For example, on my Mac it was mounted in /Volumes/Mavericks:

    df
    Filesystem     1K-blocks      Used Available Use% Mounted on
    /dev/disk0s2   249219484 145891460 103072024  59% /Volumes/Mavericks

Now copy /bin to your OS X disk:

    cp -a /bin /Volumes/<your disk name>

2. If you have a recent backup, choose "Restore From Time Machine Backup" and restore your Mac. Note that you will loose any changes you made after that backup.

3. If that's not an option, choose "Disk Utility" and select your disk from the menu on the left hand side. Then select Repair Disk:

I don't know if this will restore /bin, but it's worth a try.

Good luck.

Hold ⌘-R during startup until you see a window similar to this:

These are your options:

1. Choose Utilities>Terminal:

Your OS X disk will be mounted in /Volumes/<your disk name>. For example, on my Mac it was mounted in /Volumes/Mavericks:

    df
    Filesystem     1K-blocks      Used Available Use% Mounted on
    /dev/disk0s2   249219484 145891460 103072024  59% /Volumes/Mavericks

Now copy /bin to your OS X disk:

    cp -a /bin /Volumes/<your disk name>

Note that the contents of /bin will be outdated, as the recovery disk is not updated with the rest of the OS, so restore /bin from Time Machine after successfully starting your Mac and logging in.

2. If you have a recent backup, choose "Restore From Time Machine Backup" and restore your Mac. Note that you will loose any changes you made after that backup.

Good luck.

Boot into OS X Recovery Mode

Hold Command ⌘+R during startup until you see a window similar to this:

Back Up and Restore Options

After booting into recovery mode, these are your options:

1. Choose Utilities > Terminal:

Your OS X disk will be mounted in /Volumes/<your disk name>. For example, on my Mac it was mounted in /Volumes/Mavericks:

    df
    Filesystem     1K-blocks      Used Available Use% Mounted on
    /dev/disk0s2   249219484 145891460 103072024  59% /Volumes/Mavericks

Now copy /bin to your OS X disk:

    cp -a /bin /Volumes/<your disk name>

2. If you have a recent backup, choose Restore From Time Machine Backup and restore your Mac. Note that you will loose any changes you made after that backup.

3. If that's not an option, choose Disk Utility and select your disk from the menu on the left hand side. Then select Repair Disk:

I don't know if this will restore /bin, but it's worth a try.

Good luck.

Hold ⌘-R during startup until you see a window similar to this:

These are your options:

1. Choose Utilities>Terminal:

Your OS X disk will be mounted in /Volumes/<your disk name>. For example, on my Mac it was mounted in /Volumes/Mavericks:

    df
    Filesystem     1K-blocks      Used Available Use% Mounted on
    /dev/disk0s2   249219484 145891460 103072024  59% /Volumes/Mavericks

Now copy /bin to your OS X disk:

    cp -a /bin /Volumes/<your disk name>

2. If you have a recent backup, choose "Restore From Time Machine Backup" and restore your Mac. Note that you will loose any changes you made after that backup.

3. If that's not an option, choose "Disk Utility" and select your disk from the menu on the left hand side. Then select Repair Disk:

I don't know if this will restore /bin, but it's worth a try.

Good luck.