CS - Week 8 - Slide 18 - Arithmetic Circuits – Adders, Subtractors and Comparators

Describe a half-adder:

• State its truth table

  • use that to find which logic gates to build the half-adder

Describe a full-adder:

• State its truth table

  • use that to find which logic gates to build the full-adder

Describe how to build a full adder from half adders:

• State the truth table

Describe what is meant by a ripple-carry adder:

• State when overflow has occurred

• Describe the delay of a ripple-carry adder

Describe what is meant by a subtractor:

• Describe the underlying thought process

• introduce the idea of an n-bit subtractor/adder unit

Describe an adder/subtractor unit that will calculate S = Y - X where Y = -3 and X = 2

Describe an adder/subtractor unit that will calculate S = Y - X where Y = -3 and X = -2

Describe an adder/subtractor unit that will calculate S = Y + X where Y = -3 and X = -2

Describe how to detect overflow for signed numbers (2s complement) and unsigned numbers

Describe how to build a comparator for == and > < for:

• 2 bit numbers

• 4 bit numbers