L2 2021 - elec1601 lecture notes from 1- 5, copy from usyd canvas PDF

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L2 2021 - elec1601 lecture notes from 1- 5, copy from usyd canvas...

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ELEC1601 Foundations of Computer Systems

School of Electrical and Information Engineering

The University of Sydney

Write the procedure to translate numbers among these bases

10

8

integer in base 10 integer in base 10

result

Perform regular addition Which number is the result when considered as C'2? How would you detect freezing?

Temperature Sensor

Which operations can you perform with this circuit?

8 bits

8 bits

Which range of temperatures can you encode? Computer System bit 7

SIGN AND MAGNITUDE

1

8 bit adder circuit

bit 0

How would you add -26 (10011010) and 28 (00011100)?

Week 2: Information Encoding

ELEC1601 Foundations of Computer Systems

15

School of Electrical and Information Engineering

Sign

0 Format 1

0

0

0

0

0

Sign

Exponent

Mantissa 1

0

0

0

0

0

0

0

0

0

15

Sign

Mantissa

Exponent

0

0

Number A

0

0

1

1

1

1

1

1

1

1

0

0

0

0

0

1

0

0

0

15

0

0

0

0

0 0

0

0

0

0

0

0 0

Sign

Exponent

Mantissa

Exponent

Mantissa

15

0

Sign

Format 2 15

The University of Sydney

0

Number B

0

0

Exponent

Mantissa 1

0

0

0

0

0

0

1 0

0

0

0

0

0

0

15

15

0

0 Format 1

Sign

Maximum and mimimum exponents of the two formats?

Exponent

Mantissa

Format 2 15

0

+

0

8

-

Lower bound 1

1

1

1

1

1

1

1

1

8

Which one covers larger overall interval?

Upper bound 0

1

1

1

1

1

1

0

1

1

Exponent

Mantissa

1

1

1

1

1

1

Sign

0

1

1

1

1

1

1

Exponent

Mantissa Sign

0

First negative 1

1

0

0

0

0

0

Mantissa Sign

2

0

0

1

First positive 0

0

0

0

0

0

0

1

Exponent

0

0

0

0

0

Mantissa

0

0

1

0

0

0

0

0

0

Exponent

Sign

Week 2: Information Encoding...