Computer Science 210 Computer Organization Clocks and Memory Elements

Types of Logic Circuits Combinational –No memory –Output depends only on inputs –No state –All circuits so far, ALU, etc. have been combinational Sequential –Has memory –Memory holds state –Output depends on inputs and state

Clocks Clocks are used in sequential circuits to determine when an element should have its state updated. A clock is a free running signal that emits pulses with precise pulse width and interval. Clock cycle time is divided into two parts –When clock signal is high –When clock signal is low –The time of the changes are called edges (rising or falling)

Clocks (cont.) Edge triggered clocking – state changes occur on a clock edge (could specify rising edge or falling edge).

Clocks (cont.) General scenario is –Inputs to combinational circuit come from a state element (memory or register) –Output of combinational circuit goes into a state element –Clock cycle provides time for results of combinational component to settle.

NAND and NOR Gates A NAND B – NOT A AND B A NOR B – NOT A OR B NAND Gate A B NOR Gate A B

SR Latch Most of the time we have S=R=0. From this we can not determine Q. Check that S=R=Q=0 gives a “steady state”. Check that S=R=0, Q=1 gives a “steady state”.

SR Latch Suppose we are in State 0: S=R=Q=0. Now suppose we change S to 1. Note that Q now becomes 1 (steady). If we now change S back to 0, Q remains 1. We are now in State 1: S=R=0, Q=1. So, from State 0, we can change to State 1, by setting S to 1 and then back to 0.

SR Latch Suppose we are in State 1: S=R, Q=1. Now suppose we change R to 1. Note that Q now becomes 0 (steady). If we now change R back to 0, Q remains 0. We are now in State 0: S=R=Q=0. So, from State 1, we can change to State 0, by setting R to 1 and then back to 0.

D Latch Here C is a clock line and D is the data line. Note that if the clock is at 0, both AND gates produce 0 (S=R=0); so the SR latch keeps whatever state it is in (independent of D). Now suppose D=1, and C becomes 1. The upper AND gate produces 0, and the lower AND gate produces 1 (S=1, R=0); this sets state to State 1 (same as D). When clock goes back to 0, state does not change. If D had been 1, state would be State 1 (same as D). So state changes to D when clock is at 1.

D Flip-flop Here the first latch (master) gets its value from D when clock is high. At this point, the second latch has clock 0 so isn’t changing. When the clock pulse falls, the second latch gets its state from the output of the master latch. So state of the flip-flop changes on falling edge.

Comments Latches and flip-flops are memory elements. They have state that changes only on signal (clock signal). Latches change state whenever clock is high (could be low). Flip-flops are edge triggered.

Enable Lines To store new value, must have clock high and have the write enable line high. W

Building a Register Stores a multi-bit value Collection of D-latches are controlled by a common WE When WE = 1, n-bit value is written to the register

Building Memory 2 2 x 3 Memory address decoder word selectword WE address write enable input bits output bits