1.4.3 Boolean Algebra

• is a logic circuit which can store the value of one bit (0 or 1) • has two inputs • D : a single-bit data input • CLK : a clock signal • also has two outputs • Q : a single bit data output • ‘Q : the inverse of the data output

• is a regular pulse (change in voltage) generated by the CPU which is used to coordinate the computers components • in the D type flip flop the clock signal determines when data is captured and stored

• a clock pulse rises and falls ( rising and falling edge ) • the value of a d type flip flop (Q) can only change at a rising edge (the start of a clock tick ) • the value of Q is updates to the value of D where the clock (CLK) rises • the value/state of Q is the stored value • if the clock is not at a rising edge the output value (Q) is held and doesn’t change

• Memory Storage: Temporary data storage in processors (e.g., registers). • Counters: Implementing binary counters. • Shift Registers: Shifting data bits in serial communication. - data synchronisation

• Logic circuits that add bits together • there are two types of adders : • full adder • half adder

• used to perform the addition of 2 single bit numbers • has only 2 inputs A and B (the bits to be added) • has two outputs Sum (S) and Carry (C out) • formed from two logic gates AND and XOR

• similar to half adder but has 3 inputs instead • A, B, and an (C in) (carry input from a previous stage) • which allows a cat to be represented • produces two outputs C out and Sum (S) • two half adder can be joined with an OR gate to form a full adder [1]

• half adder adds together 2 binary digits (bits) [1] • S gives the Sum and C gives the carry [1] • 2 half adders can be joined together with an OR gate [1] • to form a full adder [1] • 4 full adders can be used to add two 4 bit numbers ( forming a ripple adder) [1] • carry output in one full adder joined to the carry input on the next stage