We have constructed an RSFQ 4-bit Arithmetic Logic Unit (ALU) in a pipelined structure. An ALU is a core element of a computer processor that performs arithmetic and logic operation on the operands in computer instruction words. We have simulated the circuit by using Josephson circuit simulation tools. We used simulation tools of XIC, $WRspice^{TM}$, and Julia. To make the circuit work faster, we used a forward clocking scheme. This required a careful design of timing between clock and data pulses in ALU. The RSFQ 1-bit block of ALU used in constructing the 4-bit ALU was consisted of three DC current driven SFQ switches and a half-adder. By commutating output ports of the half adder, we could produce AND, OR, XOR, or ADD functions. The circuit size of the 4-bit ALU when fabricated was 3 mm x 1.5 mm, fitting in a 5 mm x 5mm chip. The fabricated 4-bit ALU operated correctly at 5 GHz clock frequency. The chip was tested at the liquid-helium temperature.