1.4.3 Boolean Algebra
Boolean Algebra — Note 5 of 5
Candidates need to understand the purpose and principles of D type flip flops and how and where they are used in a computer. They should be able to recognise how they can be triggered by a clock pulse (see practice paper 2 for an example). Candidates are not expected to memorise the logic gates that make up a D-type flip flop. Candidates need to understand the purpose and function of an adder circuit, and the difference between a half and full adder. They should be able to recognise and draw the logic gates and truth tables for full and half adders.
Logic gates can be combined into circuits with useful jobs. Adders carry out binary addition inside the ALU, and D-type flip-flops store a single bit, forming the basis of registers and memory.
Exam tipCommon mistake
Adds two bits, giving a Sum and a Carry. Sum = A ⊻ B; Carry = A ∧ B.
Adds two bits PLUS a carry in, giving a Sum and a Carry out. Sum = A ⊻ B ⊻ Cin; Cout = (A ∧ B) ∨ (Cin ∧ (A ⊻ B)).
A circuit that stores one bit. On each rising edge of the clock pulse, the output Q takes the value of the data input D, and keeps it until the next clock pulse.
Half adder Full adder
A B | C S A B Cin | Cout S
0 0 | 0 0 0 0 0 | 0 0
0 1 | 0 1 0 0 1 | 0 1
1 0 | 0 1 0 1 0 | 0 1
1 1 | 1 0 0 1 1 | 1 0
1 0 0 | 0 1
1 0 1 | 1 0
1 1 0 | 1 0
1 1 1 | 1 1