That's a simple question with a really complex answer. Most economics questions turn out that way.

Constantinople was a fabulously wealthy city during the Roman and Middle Ages. It sat on the crossroads to Asia and was in a perfect position to dominate trade. The rulers of the city saw this opportunity and took full advantage of it, creating a monopoly on coinage and trade. This brought in huge sums of gold coins into the empire, allowing Constantinople to be considered one of the most powerful economic centers of the time.

Their coins were fairly standard for the time, printing gold, silver and copper coins. As the empire waned, the gold became more and more diluted as emperors attempted to prop up the economy. Arabic conquests, Venetian bankers/traders and the Crusades did the Byzantines no favors and eventually crippled the city. By the early 1300's, the gold coin was abandoned in favor of silver coins.

By now, Venitian coins were penetrating into the Empire and intermixed, destroying the monopoly of coinage.

We have records that in 1370, the Empire owed Venice 25,663 hyperpyra, of which only about 4,000 had been paid. They were in debt with a shrinking economy that was being attacked on all sides. Their coinage had fallen out of favor and they were soon to be swallowed up by the Ottoman Empire.

The coins at the end of the Empire's life were not worth very much. The coins during its golden era were worth a great deal. There were times that other nations were in the Empire's debt and times where it owed money to other nations. It survived too long to make a sweeping claim that it was never in debt.

W. Treadgold, A History of the Byzantine State and Society

Harris, Byzantium and The Crusades

Morrisson, Byzantine Money

I'm not an expert on the Byzantine Empire, but I can address a point you raised in the comments: "the Byzantine Empire never went into debt because they never abandoned the Gold Standard." From an economics standpoint, that's complete hooey (it's a technical term). Here's why.

First, that point conflates or gives a causal relationship to two totally independent and non-causal factors: the state's existence as a borrower or creditor nation, and the state's use of shiny metal as the bedrock of their currency. For most of its history, the U.S. adhered to the gold standard. So, we can ask: did adherence to the gold standard prevent the U.S. from going into debt? And because U.S. government debt records are a bit more accessible than Byzantine records, we can answer that question loudly and clearly: absolutely not. Between 1790 and 1918, the U.S. was frequently in debt, despite adherence to the gold standard. Investigation of the historic debt of the governments of Spain and Portugal would further shore up a simple conclusion: countries with gold standard currencies go into debt frequently. So we know there's no connection between debt and the gold standard.

Second, I'm a bit interested in the book that made the claim. In recent years, primarily in the U.S., there's been increasing interest in a return to the gold standard, driven largely by some populist politicians who shall remain nameless. It's critically important to note that there is overwhelming consensus among economists that the gold standard is an absolutely horrible idea. There's a nice summary-level article in The Atlantic on the topic [http://www.theatlantic.com/business/archive/2012/08/why-the-gold-standard-is-the-worlds-worst-economic-idea-in-2-charts/261552/] and you can also read some accessible writing by actual economists on the subject, like Mayer, David A., "The Everything Economics Book: From theory to practice, your complete guide to understanding economics today," pp. 33–34 (2010); or Paul Krugman's article for Slate, [http://www.slate.com/articles/business/the_dismal_science/1996/11/the_gold_bug_variations.html]. I mention this only because your book is making a plainly (and easily-demonstrable) false contention, and I wonder if it's doing so as part of this fringe-y advance of the gold standard.

This is most defently NOT true.

The Byzantine Empire had both debt and inflation at diffrent times. They lanched or relunched diffrent gold and silver coins because the earlier version had degrated into bad quality. I am not a expert on history of coins. The Byzantine coins were very wide spread and stable sometimes and sometimes not. As for debt, its also false. During major crisis the governemnt had to lend money, mostly from the church.

The error probebly happened because the Byzantine Empire was really good at using money and getting people to use it. They had keeped the old roman traditions in taxation and montary economy alife. This allowed them to have efficant taxation and regularity. The had a simple form of a budget each year. This meant that they could avoid the massiv debt many kingdoms/empires had to threw themself into to finance some programm (war, building).

In summation, they had an efficent montary economy and taxation for long periods and that allowed them to have the economc edge often. This however does not mean that they never had inflation or debt.

This is a bit of a side question, but can anyone give any good book or reading suggestions on the popularity of different coins in different eras and why they were popular/fell out of popularity?