The Princess Royal, the battalion's Royal Colonel, also presented medals at the Palace of Holyroodhouse.
Members of the battalion have recently returned from Afghanistan, where they mentored the national army.
Three soldiers from the battalion were killed in the tour, which began in September.
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Haughey was commissioned by his colonel to take photographs of the battalion for Army and civilian newspapers.
The battalion were deployed in September last year and got back to the UK earlier this month.
The battalion was awarded the honour at a special ceremony in Victoria Square, at about 13:00 BST.
Their mission is mentoring the Afghan National Army, and the battalion has teams spread across Helmand Province.
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They were among some 350 soldiers from the battalion which was on its first operational tour in 1994-1995.
He said parcels of gifts were sent by its residents while the battalion was on operations in Afghanistan.
Three soldiers from the battalion died in separate incidents in a tour which lasted for more than six months.
The battalion fought the Turks in Mesopotamia until the end of the war.
The MOI captured 70 from the Battalion 16, which is very dangerous battalion.
I've seen the damage to some and heard of the damage to the rest of the aircraft in the battalion.
When his commander was killed, Wolff took charge of the battalion of 3, 000 Americans and led an offensive into the Sierra Pandols.
Boros is all about hitting the ground running with high power creatures that attack early and often, fueled by the battalion mechanic.
The battalion moved back to Fort George in 2007 after eight years, during which they were stationed in Northern Ireland and Germany.
It was the first time the battalion had been posted to Afghanistan.
Fire Support Company was one of three units making up the battalion, which recruits from around Wales although it is based in Tidworth, Wiltshire.
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Having the freedom of the the town means the battalion is allowed to parade with colours flying, bayonets fixed, drums beating and bands playing.
BBC: 2nd Battalion The Royal Welsh: Soldiers in Bridgend march
There are currently 137 soldiers from the battalion remaining in Afghanistan.
In December, shortly before the battalion shipped out for Afghanistan, Bravo Company commander Brent Jones gathered his 170 men outside the brick headquarters building at Camp Lejeune, N.
Elwood is the battalion clerk in an antiquated peacetime outfit, and, in the absence of combat, he devotes his skills to the black market and the heroin trade.
Asked after the inquest about Mrs Gray's concerns over the body armour, Captain Ian Robinson said the battalion were the "best protected soldiers in the British Army" when deployed to Afghanistan.
He joined the battalion's march through Clitheroe on Thursday.
The battalion was deployed to Afghanistan in September 2010.
"He was one of the Battalion's great characters, always smiling and always ready to brighten the mood with his fellow Fusiliers, " Warrant Officer Ned Miller of the 2nd Fusiliers said in a statement.
In previous tours in 2009, the battalion lost Lance Corporal Chris Harkett when he was killed by an improvised explosive device (IED) as he provided covering fire on a Taliban stronghold near Musa Qala.
Cpl William Savage, of the Royal Highland Fusiliers, the 2nd Battalion The Royal Regiment of Scotland, and Pte Robert Hetherington, of the 51st Highland, 7th Battalion, a Territorial Army member, also died in the explosion.
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