```python
from seedemu.core import Emulator, Merger
from seedemu.layers import Base, Routing, Ebgp
from seedemu.services import DomainNameCachingService, DomainNameCachingServer, DefaultDomainNameCachingServiceMerger

# Create the base layer
base = Base()

# Create autonomous systems and internet exchanges
asns = [100, 200, 300]
ixps = ['ixp1', 'ixp2']

for asn in asns:
    asys = base.createAutonomousSystem(asn)
    router = asys.createRouter('router1')
    network = asys.createNetwork('net1')
    hosts = asys.createHosts('host', 3)
    for host in hosts:
        network.connect(host)
    network.connect(router)
    for ixp in ixps:
        base.getInternetExchange(ixp).connect(router)

# Domain name caching service
dns = DomainNameCachingService()

# Install DNS caching server on specific hosts
for asn in asns:
    host = base.getNodeByAsnAndName(asn, 'host1')
    dns.install('dns{}'.format(asn), host)

# Add bindings
dns.addBinding('dns100', 'example.com', '1.1.1.1')
dns.addBinding('dns200', 'example.net', '2.2.2.2')
dns.addBinding('dns300', 'example.org', '3.3.3.3')

# Routing layer
routing = Routing()

# eBGP layer
ebgp = Ebgp()

# Add private peerings between ASes
ebgp.addPrivatePeering(100, 200, 'ixp1')
ebgp.addPrivatePeering(200, 300, 'ixp2')

# Create the emulator
emu = Emulator()

# Add layers to the emulator
emu.addLayer(base)
emu.addLayer(routing)
emu.addLayer(ebgp)
emu.addLayer(dns)

# Merge services
merger = Merger()
merger.addMerger(DefaultDomainNameCachingServiceMerger())

# Merge and compile the emulation
emu.compile(merger=merger)

# Dump the state of the emulator to a binary file
emu.dump('emulation.bin')
```