In a digital memory with an array of bit cells coupled to word lines and bit lines, each bit cell having cross coupled inverters isolated from bit lines by passing gate transistors until addressed, some or all of the bit cells are switchable between a sleep mode and a standby mode in response to a control signal. A bit line bias circuit controls the voltage at which the bit lines are caused to float when in the sleep mode. A pull-up transistor for each bit line BL or BLB in a complementary pair has a conductive channel coupled to a positive supply voltage and a gate coupled to the other bit line in the pair, BLB or BL, respectively. A connecting transistor also can be coupled between the bit lines of the complementary pair, bringing the floating bit lines to the supply voltage less a difference voltage ΔV.