echo $'\0' >a does not write the nul byte

[hans]

Configuration Information [Automatically generated, do not change]:
Machine: x86_64
OS: linux-gnu
Compiler: gcc
Compilation CFLAGS:  -DPROGRAM='bash' -DCONF_HOSTTYPE='x86_64' 
-DCONF_OSTYPE='linux-gnu' -DCONF_MACHTYPE='x86_64-pc-linux-gnu' 
-DCONF_VENDOR='pc' -DLOCALEDIR='/usr/share/locale' -DPACKAGE='bash' -DSHELL 
-DHAVE_CONFIG_H   -I.  -I../bash -I../bash/include -I../bash/lib  
-D_FORTIFY_SOURCE=2 -g -O2 -fstack-protector --param=ssp-buffer-size=4 -Wformat 
-Werror=format-security -Wall
uname output: Linux artax 3.2.0-4-amd64 #1 SMP Debian 3.2.96-2 x86_64 GNU/Linux
Machine Type: x86_64-pc-linux-gnu

Bash Version: 4.2
Patch Level: 37
Release Status: release

Description:
        Command
                echo $'\0' |od -c
        writes
                0000000  \n
                0000001
        in contrast to
                echo $'\1' |od -c
                0000000 001  \n
                0000002
        The nul byte is not echoed by $'\0'.

Repeat-By:
        echo $'\0' |od -c
        echo $'\1' |od -c