An apparatus comprising: a processing component to perform an operation based on information specified in a control table stored in a memory system, the control table comprising a plurality of entries each specifying a first limit address and one of a second limit address and a size, for identifying limits of a corresponding address region of variable size within an address space, where the plurality of entries are arranged in the control table in order of the first limit address; and table lookup circuitry to perform a binary search procedure to identify whether the control table comprises an entry corresponding to a query address, the binary search procedure comprising a plurality of search window narrowing steps for narrowing a current search window of candidate entries of the control table to a narrower search window comprising fewer candidate entries; in which: in a given search window narrowing step, the table lookup circuitry is configured to narrow the current search window based on a comparison of the query address against the first limit address of a selected candidate entry of the current search window, independent of said one of the second limit address and the size of the selected candidate entry; and following a final search window narrowing step which narrows the current search window to a single candidate entry of the control table, the table lookup circuitry is configured to determine that said single candidate entry is the entry corresponding to the query address when the query address is within the corresponding address region defined by the first limit address and said one of the second limit address and the size of said single candidate entry; in which for each entry, the table lookup circuitry is configured to permit the variable size to be a number of bytes other than a power of 2. a processing component to perform an operation based on information specified in a control table stored in a memory system, the control table comprising a plurality of entries each specifying a first limit address and one of a second limit address and a size, for identifying limits of a corresponding address region of variable size within an address space, where the plurality of entries are arranged in the control table in order of the first limit address; and table lookup circuitry to perform a binary search procedure to identify whether the control table comprises an entry corresponding to a query address, the binary search procedure comprising a plurality of search window narrowing steps for narrowing a current search window of candidate entries of the control table to a narrower search window comprising fewer candidate entries; in which: in a given search window narrowing step, the table lookup circuitry is configured to narrow the current search window based on a comparison of the query address against the first limit address of a selected candidate entry of the current search window, independent of said one of the second limit address and the size of the selected candidate entry; and following a final search window narrowing step which narrows the current search window to a single candidate entry of the control table, the table lookup circuitry is configured to determine that said single candidate entry is the entry corresponding to the query address when the query address is within the corresponding address region defined by the first limit address and said one of the second limit address and the size of said single candidate entry; in which for each entry, the table lookup circuitry is configured to permit the variable size to be a number of bytes other than a power of 2. in a given search window narrowing step, the table lookup circuitry is configured to narrow the current search window based on a comparison of the query address against the first limit address of a selected candidate entry of the current search window, independent of said one of the second limit address and the size of the selected candidate entry; and following a final search window narrowing step which narrows the current search window to a single candidate entry of the control table, the table lookup circuitry is configured to determine that said single candidate entry is the entry corresponding to the query address when the query address is within the corresponding address region defined by the first limit address and said one of the second limit address and the size of said single candidate entry; in which for each entry, the table lookup circuitry is configured to permit the variable size to be a number of bytes other than a power of 2.