The Expert Infantryman Badge, or EIB, is a military badge of the United States Army. It is the non-combat equivalent to the Combat Infantryman Badge. The primary difference between the decorations is the Combat Infantryman Badge (CIB) is awarded for participation in infantry ground combat, while the Expert Infantryman Badge is presented for completion of an approved Army course of testing.
The EIB was first created in October 1943. It is awarded to U.S. Army personnel who hold infantry or special forces military occupational specialities. To be awarded the EIB, the service member must complete a testing phase which is the culmination of weeks of training, leading to a final evaluation period. The EIB test is administered on the average once per year with pass rates averaging no more than 50 percent, depending on the unit conducting testing. Due to the rigid testing procedures, many holders of the EIB value it more than the CIB.
Personnel who have been awarded both the EIB and the CIB are not authorized to wear both decorations simultaneously. In such cases, the CIB has precedence according to Army Regulation 670-1.
A similar decoration exists for medical personnel, known as the Expert Field Medical Badge.
The above speaks about WEARING, not display cases.
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I'm sure we'll find out more about the gentleman in question, and we'll hopefully have him post the info in another section when we get him to join! 
Proud Daughter of Walter (Monday) Poniedzialek
540th Engineer Combat Regiment, 2833rd Bn, H&S Co, 4th Platoon
There's "No Bridge Too Far"