Decimal arithmetic is often used in commercial, financial, and Internet-based applications. Due to the growing importance of decimal floating-point (DFP) arithmetic, the IEEE 754-2008 Standard for Floating-Point Arithmetic (IEEE 754-2008) includes specifications for DFP arithmetic. IBM recently announced adding DFP instructions to their POWER6, z9, and z10 microprocessor architectures. As processor support for DFP arithmetic emerges, it is important to investigate efficient arithmetic algorithms and hardware designs for common DFP arithmetic operations. This paper gives an overview of DFP arithmetic in IEEE 754-2008 and discusses previous research on decimal fixed-point and floating-point addition. It also presents novel designs for a DFP adder and a DFP multifunction unit (DFP MFU) that comply with IEEE 754-2008. To reduce their delay, the DFP adder and MFU use decimal injection-based rounding, a new form of decimal operand alignment, and a fast flag-based method for rounding and overflow detection. Synthesis results indicate that the proposed DFP adder is roughly 21 percent faster and 1.6 percent smaller than a previous DFP adder design, when implemented in the same technology. Compared to the DFP adder, the DFP MFU provides six additional operations, yet only has 2.8 percent more delay and 9.7 percent more area. A pipelined version of the DFP MFU has a latency of six cycles, a throughput of one result per cycle, an estimated critical path delay of 12.9 fanout-of-four (F04) inverter delays, and an estimated area of 45, 681 NAND2 equivalent gates.