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Below is the configuration for DHCP in Cisco's IOS.

R1#sh run | s dhcp
ip dhcp excluded-address 192.168.0.1 192.168.0.49
ip dhcp pool MYNETWORK
   network 192.168.0.0 255.255.255.0
   default-router 192.168.0.1 
R1#

Relays are configured with ip helper-address x.x.x.x to specify which address to forward received DHCP requests. When our RTR forwards a DHCP request out via Relay, it does so with the SOURCE ADDRESS of the INTERFACE the HELPER-ADDRESS command was configured on. When this happens, the DHCP server can look at the SOURCE ADDR of the packet, and know exactly which scope to lease an address from - the same network that source resides in, ofc.

The helper address is configured on the interface connected to the subnet which does not contain the DHCP server.

interface FastEthernet0/1
 ip address 172.16.0.1 255.255.255.0
 ip helper-address 192.168.1.1
 duplex auto
 speed auto
end

R1#sh ip dhcp binding 
Bindings from all pools not associated with VRF:
IP address          Client-ID/	 	    Lease expiration        Type
		    Hardware address/
		    User name
172.16.0.2          0063.6973.636f.2d63.    Mar 01 2002 12:06 AM    Automatic
                    3230.342e.3430.3930.
                    2e30.3030.312d.4661.
                    302f.31
192.168.1.50        0063.6973.636f.2d63.    Mar 02 2002 12:01 AM    Automatic
                    3230.332e.3366.6461.
                    2e30.3030.302d.4661.
                    302f.30

R1#sh ip dhcp server statistics 
Memory usage         25022
Address pools        2
Database agents      0
Automatic bindings   2
Manual bindings      0
Expired bindings     0
Malformed messages   0
Secure arp entries   0

Message              Received
BOOTREQUEST          0
DHCPDISCOVER         11
DHCPREQUEST          1
DHCPDECLINE          0
DHCPRELEASE          0
DHCPINFORM           0

Message              Sent
BOOTREPLY            0
DHCPOFFER            8
DHCPACK              1
DHCPNAK              0

Note that excluded address ranges are not deducted from the Total addresses field in the output.

R1#sh ip dhcp pool 

Pool LAN :
 Utilization mark (high/low)    : 100 / 0
 Subnet size (first/next)       : 0 / 0 
 Total addresses                : 254
 Leased addresses               : 1
 Pending event                  : none
 1 subnet is currently in the pool :
 Current index        IP address range                    Leased addresses
 192.168.1.51         192.168.1.1      - 192.168.1.254     1