Arithmetic Circuits

Arithmetic Circuits. Didn’t I learn how to do addition in the second grade? UNC courses aren’t what they used to be. 01011 +00101 10000. Finally; time to build some serious functional blocks. We’ll need a lot of boxes. Review: 2’s Complement. N bits. -2 N-1. 2 N-2. …. …. …. 2 3.

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Combinational Arithmetic Circuits

Combinational Arithmetic Circuits. Addition: Half Adder (HA). Full Adder (FA). Carry Ripple Adders. Carry Look-Ahead Adders. Subtraction: Half Subtractor. Full Subtractor. Borrow Ripple Subtractors. Subtraction using adders. Multiplication: Combinational Array Multipliers. X 0 0 1

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COMP541 Arithmetic Circuits

COMP541 Arithmetic Circuits. Montek Singh (Not covered). Today ’ s Topics. Adder circuits ripple-carry adder (revisited) more advanced: carry- lookahead adder Subtraction by adding the negative Overflow. Iterative Circuit. Like a hierarchy , except functional blocks per bit. Adders.

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Number and Arithmetic Circuits

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Arithmetic Circuits

Arithmetic Circuits. Half Adder. Half Adder. Full Adder. Full Adder. Implementing a Full adder using two half adders. Parallel Binary Adder. Parallel Binary adder Two Numbers X & Y Each number is represented using 6 bits. [X]=X o X 1 X 2 X 3 X 4 X 5 [Y]=Y o Y 1 Y 2 Y 3 Y 4 Y 5.

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Arithmetic Functions and Circuits

Arithmetic Functions and Circuits. The initial carry in is implicitly 0. 1 1 1 0 Carry in 1 0 1 1 Augend + 1 1 1 0 Addend 1 1 0 0 1 Sum. most significant bit , or MSB. least significant bit , or LSB. Binary Addition by Hand.

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Arithmetic Circuits

Arithmetic Circuits. Combinational Circuits. Combinational circuit is a circuit in which the different gates are combined in the circuit, for example encoder, decoder, multiplexer and de-multiplexer. Some of the characteristics of combinational circuits are following −

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Arithmetic Circuits II

Arithmetic Circuits II. Multiplier. Given the multiplicand, B = {B 1 B 0 } and the multiplier A = {A 1 A 0 } Then we multiply by doing single-bit multiplications and shifts. AND computes A 0 B 0. A. 0. B. B. 1. 0. A. 1. B. B. 1. 0.

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Arithmetic Circuits II

Arithmetic Circuits II. Anselmo Lastra. Overflow. Two cases of overflow for addition of signed numbers Two large positive numbers overflow into sign bit Not enough room for result Two large negative numbers added Same – not enough bits Carry out can be OK. Examples. 4-bit signed numbers

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Arithmetic Operations

Arithmetic Operations. Arithmetic Operations addition subtraction multiplication division Each of these operations on the integer representations: unsigned two's complement. Addition. One bit of binary addition. carry in. a. carry out. +. b. sum bit. Addition Truth Table.

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Arithmetic Circuits I

Arithmetic Circuits I. Iterative Circuit. Like a hierachy, except functional blocks per bit. Adders. Great example of this type of design Design a 1-bit adder circuit, then expand to n-bit adder Look at Half adder – which is a 2-bit adder, no carry in Inputs are bits to be added

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Chap. 6 Digital Arithmetic: Operations & Circuits

Chap. 6 Digital Arithmetic: Operations & Circuits. Introduction This chapter will be concentrate on how computers perform the basic arithmetic operations 6-1 Binary Addition Addition is the most important operation in digital systems

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Arithmetic Circuits

Arithmetic Circuits. Didn’t I learn how to do addition in the second grade? UNC courses aren’t what they used to be. 01011 +00101 10000. Finally; time to build some serious functional blocks. We’ll need a lot of boxes. Reading: Study Chapter 3. Review: 2’s Complement. N bits. -2 N-1.

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Arithmetic Operations

Arithmetic Operations. Arithmetic Operations. Signed/unsigned integer 64-bit 96-bit (extended precision) Floating-point 32-bit (single precision) 64-bit (double precision) 128-bit (quadraple precision) 64-bit logical operations. Integer Operations. Signed Integer

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Arithmetic Circuits I

Arithmetic Circuits I. Iterative Combinational Circuits. Like a hierachy, except functional blocks per bit. Adders. Great example of Iterative design Design a 1-bit adder circuit, then expand to n-bit adder Look at Half adder – which is a 2-bit adder Inputs are bits to be added

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Arithmetic circuits

Arithmetic circuits. Binary addition Binary Subtraction Unsigned binary numbers Sign-magnitude numbers 2 ’ S Complement representation 2 ’ S Complement arithmetic Arithmetic building blocks. Powers of 2 2 0 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 2 10 2 11 2 12 2 13 2 14 2 15

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Ch. 6 Digital Arithmetic and Arithmetic Circuits

Ch. 6 Digital Arithmetic and Arithmetic Circuits. 이 상 훈 경남대학교 전기전자공학부. 단원목차. 6.1 Digital Arithmetic 6.2 Signed Binary Numbers 6.3 Signed Binary Arithmetic 6.4 Hexadecimal Arithmetic 6.5 Numeric and Alphanumeric Codes 6.6 Binary Adders and Subtractors 6.7 BCD Adders

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Arithmetic Operations

Arithmetic Operations. Add and subtract, three operands Two sources and one destination add a, b, c # a gets b + c All arithmetic operations have this form Design Principle 1: Simplicity favors regularity Regularity makes implementation simpler

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Chapter 6 – Digital Arithmetic: Operations & Circuits

Chapter 6 – Digital Arithmetic: Operations & Circuits. Chapter 6 Objectives. Selected areas covered in this chapter : Binary addition, subtraction, multiplication, division. Differences between binary addition and OR addition.

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Chapter 6 – Digital Arithmetic: Operations & Circuits

Chapter 6 – Digital Arithmetic: Operations & Circuits. Chapter 6 Objectives. Selected areas covered in this chapter : Binary addition, subtraction, multiplication, division. Differences between binary addition and OR addition.

609 views • 50 slides

Arithmetic Circuits I

Arithmetic Circuits I. Iterative Combinational Circuits. Like a hierachy, except functional blocks per bit. Adders. Great example of Iterative design Design a 1-bit adder circuit, then expand to n-bit adder Look at Half adder – which is a 2-bit adder Inputs are bits to be added

388 views • 36 slides

Arithmetic Circuits

Arithmetic Circuits. Half Adder. Half Adder. Full Adder. Full Adder. Implementing a Full adder using two half adders. Parallel Binary Adder. Parallel Binary adder Two Numbers X & Y Each number is represented using 6 bits. [X]=X o X 1 X 2 X 3 X 4 X 5 [Y]=Y o Y 1 Y 2 Y 3 Y 4 Y 5.

311 views • 23 slides