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The paper describes the Mark II digital-computing machine now operating in the Computing Machine Laboratory of Manchester University. It has a 100 kc/s parallel cathode-ray-tube store and a 1 Mc/s serial control, B-register and accumulator. Thus, internally, the speed of the machine is inherently greater than that of its predecessor by a factor of ten. Orders which concern the B-register or control are extracted from the store and obeyed in 60 microsec. The machine has a floating-point accumulator, numbers being represented in the form x2y where x and y are respectively 30 and 10 digits in length. Numbers to be added to the accumulator are automatically shifted appropriately before addition; they are then added and the sum is standardized. An order involving such a floating-point addition is extracted from the store and obeyed in 180 microsec. Similar remarks apply to subtraction. For multiplication, which involves floating-point addition to, or subtraction from, the accumulator, the corresponding time is 360 microsec. The number of thermionic cathodes in the Mark II machine is 57% less than that in the Mark I machine. A comparison is made between the Mark II machine and a possible fixed-point version of it, so that the true importance of the floating-point accumulator can be ascertained.