We have developed and tested an RSFQ 4-bit Arithmetic Logic Unit (ALU) based on half adder cells and de switches. ALU is a core element of a computer processor that performs arithmetic and logic operations on the operands in computer instruction words. The designed ALU had limited operation functions of OR, AND, XOR, and ADD. It had a pipeline structure. We have simulated the circuit by using Josephson circuit simulation tools in order to reduce the timing problem, and confirmed the correct operation of the designed ALU. We used simulation tools of $XIC^{TM},;WRspice^{TM}$, and Julia. The fabricated 4-bit ALU circuit had a size of $3000{ cal}um{ imes}1500{cal}$, and the chip size was $5{cal} mm{ imes}5{cal}mm$. The test speeds were 1000 kHz and 5 GHz. For high-speed test, we used an eye-diagram technique. Our 4-bit ALU operated correctly up to 5 GHz clock frequency. The chip was tested at the liquid-helium temperature.