A multi-bit gray code generation circuit includes: a zeroth bit gray code generation circuit configured to generate a gray code corresponding to a bit 0 of a multi-bit gray code; and a plurality of gray code generation circuits each configured to generate a gray code corresponding to each bit higher than the bit 0 of the multi-bit gray code. Each of the plurality of gray code generation circuits is constituted by a plurality of flip-flop circuits. An output of a flip-flop circuit in the previous stage is input to a flip-flop circuit of the next stage. An output of a flip-flop circuit of the final stage is inverted and held by a flip-flop circuit of the first stage. An output of one of the plurality of flip-flop circuits is output as a gray code corresponding to each bit.

A bi-directional Gray code counter includes a first set of logic circuitry configured to receive an input having a first sequence of bits representing a first value. The first set of logic circuitry is further configured to convert the first sequence of bits to a second sequence of bits representing the first value. The bi-directional Gray code counter further includes a second set of logic circuitry and third second set of logic circuitry. The second set of logic circuitry is configured to compare the second sequence of bits to a bit index pattern. The third set of logic circuitry is configured to transition one bit in the first sequence of bits from a first state to a second state to form a third sequence of bits representing a second value. The one bit is transitioned in response to the second sequence of bits being compared to the bit index pattern.

A synchronizer that can generate pipeline (e.g., FIFO, LIFO) status in a single step without intermediate synchronization. The status can be an indicator of whether a pipeline is full, empty, almost full, or almost empty. The synchronizer (also referred to as a double-sync or ripple-based pipeline status synchronizer) can be used with any kind of clock crossing pipeline and all kinds of pointer encodings. The double-sync and ripple-based pipeline status synchronizers eliminate costly validation and semi-manual timing closure, suggests better performance and testability, and have lower area and power.

Embodiments of the present invention relate to an architecture that uses hierarchical statistically multiplexed counters to extend counter life by orders of magnitude. Each level includes statistically multiplexed counters. The statistically multiplexed counters includes P base counters and S subcounters, wherein the S subcounters are dynamically concatenated with the P base counters. When a row overflow in a level occurs, counters in a next level above are used to extend counter life. The hierarchical statistically multiplexed counters can be used with an overflow FIFO to further extend counter life.

Disclosed are systems and methods for providing programming of multi-level memory cells using an optimized multiphase mapping with a balanced Gray code. A method includes programming, in a first phase, a first portion of data into memory cells in a first-level cell mode. The method may also include reading, from the memory cells, the programmed first portion of the data. The method may also include programming, in a second phase, a second portion of the data into the memory cells in a second-level cell mode, wherein programming the second phase is based on applying, to the read first portion of the data, a mapping from the first-level cell mode to the second-level cell mode. The mapping may be selected based on minimizing an average voltage change of the memory cells from the first to second phase while maintaining a balanced Gray code.

An image sensor includes a pixel sensor that senses an incident light and outputs a sampling signal of an analog shape, a sampler that compares the sampling signal and a ramp signal and outputs a comparison signal being time-axis length information, and a gray counter that counts a length of the comparison signal in synchronization with a clock signal and outputs a digital value. The gray counter includes a first flip-flop that divides the clock signal by 2 and generates a first gray code signal, a second flip-flop that delays a first data signal being a four-divided signal of the clock signal and outputs a second gray code signal, and a third flip-flop that delays the second gray code signal being two-divided and outputs a third gray code signal.

A tracker circuit configured to provide a variable supply voltage to a power amplifier (PA) circuit is disclosed. The tracker circuit includes a state machine circuit comprising a plurality of states mapped in accordance with transitions associated with a mapping scheme. In some embodiments, the plurality of states of the state machine circuit identify one or more operational modes associated with the tracker circuit, wherein at least one operational mode comprises one or more voltage levels respectively associated therewith. In some embodiments, the one or more operational modes includes at least two active operational modes. In some embodiments, a transition between the one or more operational modes of the tracker circuit is controlled by a digital selection signal received from a digital communication interface associated therewith.

A multi-bit gray code generation circuit includes: a zeroth bit gray code generation circuit configured to generate a gray code corresponding to a bit 0 of a multi-bit gray code; and a plurality of gray code generation circuits each configured to generate a gray code corresponding to each bit higher than the bit 0 of the multi-bit gray code. Each of the plurality of gray code generation circuits is constituted by a plurality of flip-flop circuits. An output of a flip-flop circuit in the previous stage is input to a flip-flop circuit of the next stage. An output of a flip-flop circuit of the final stage is inverted and held by a flip-flop circuit of the first stage. An output of one of the plurality of flip-flop circuits is output as a gray code corresponding to each bit.

A request to perform a read operation on a memory device is received. The memory device includes a first group of memory cells. The first group of memory cells represents a first sequence of bits based on a first sequence of charge levels formed by the first group of memory cells. The read operation is performed by obtaining a first read signal for a first memory cell and a second read signal for a second memory cell of the first group of memory cells. A first rule logic is applied to the first read signal to generate a first updated signal and a second rule logic is applied to the second read signal to generate a second updated signal. Logic functions are applied to the first and second updated signals to generate an output signal indicating the first sequence of bits stored by the first group of memory cells.

An image sensor includes a pixel sensor that senses an incident light and outputs a sampling signal of an analog shape, a sampler that compares the sampling signal and a ramp signal and outputs a comparison signal being time-axis length information, and a gray counter that counts a length of the comparison signal in synchronization with a clock signal and outputs a digital value. The gray counter includes a first flip-flop that divides the clock signal by 2 and generates a first gray code signal, a second flip-flop that delays a first data signal being a four-divided signal of the clock signal and outputs a second gray code signal, and a third flip-flop that delays the second gray code signal being two-divided and outputs a third gray code signal.