Using building blocks to make bigger circuits So far we have defined basic building blocks as Inverter, AND, and OR gates storage elements (D-Flip-flop) These building blocks can be used to bigger circuits We may give them additional functionality We can either add more inputs or wider inputs, and outputs Or we may perform a more complex operation Or both, like multiplexers, decoders, …. Examples: 3, 4, 5 …. n bit input gates Or you may have multiple bit data inputs AND, OR, XOR, STORE, READ n-bit data

Making a register C D Q P D0 D1 D2 D3 Clock Q0 Q1 Q2 Q3 Flip-flops can be connected to act as a register All clock signals are connected together to one clock All flip-flops get different input, each storing one-bit information A 4-bit register is shown -- It uses 4 D-FFs Has a 4 bit inputs and 1 clock and produces 4 bit output C D Q P D0 D1 D2 D3 Clock Q0 Q1 Q2 Q3

Making a shift-register Flip-flops can also be connected to act as a shift register All clock signals are connected together to one clock First flip flop gets a new input Others get input from previous flip-flop A 4-bit shift register is shown It has one bit and one clock input and produces 1 bit output D0 C D Q P Clock Q0 Q1 Q2 Q3

Using 1-bit building blocks to make n-bit circuit Design a 1 bit circuit with proper “glue logic” to use it for n-bits It is called a bit slice The basic idea of bit slice is to design a 1-bit circuit and then piece together n of these to get an n-bit component Previous two examples showed how to use 1-bit components However, there was no other glue signal or logic Next, we consider other kind of examples A half-adder adds two 1-bit inputs Two half adders can be used to add 3 bits A 3-bit adder is a full adder B C S A

Full adder and multi-bit adder Two half adders can be used to add 3 bits n-bit adder can use full adders n can be arbitrary large Cout0 Sum0 A0 B0 Ci Full Adder Cout1 Sum1 A1 B1 C1 Cout2 Sum2 A2 B2 C2 Cout3 Sum3 A3 B3 C3 B C S A B C S A Cout Sum Cout Sum A B C Full Adder

Glue Logic Normally the glue logic is part of 1-bit adder A basic building block has Primary inputs Primary outputs Cascading inputs Cascading outputs The cascading signals interact directly with the glue logic Carry in 1-bit adder is a primary as well as a cascading output A and B are primary inputs C is a cascading input Cout is cascading output S is primary output