Conventional electronics technology uses an electron's charge to store information and a current of electrons to transfer information. Spintronics technology, in contrast, uses an electron's 'spin' in addition to its charge to transfer and store information. Magnetic Tunnel Junctions (MTJ) are spintronic devices that exhibit two distinct resistance states due to the tunneling magnetoresistance (TMR) effect. Their properties can provide significant advantages over conventional electronics in the design of computer systems. We characterize some of the challenges in using spintronic technology in large systems, and describe a novel design technique called 'union with neutralization' to combine individual component designs into multi-functional units. We use this technique to present the design of an arithmetic and logical unit (ALU) using 20 MTJs and two CMOS-based sense amplifiers. The spintronics-based ALU has the potential to offer considerable area, timing, and power advantages over a conventional CMOS-based ALU.