Integer Representation

Software Developers View of Hardware Integer Representation

Syllabus ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

What is Integer Representation About? ,[object Object],[object Object],[object Object],[object Object],[object Object]

How can we represent a binary number? ,[object Object],[object Object],[object Object],NO

How can we represent a binary number? ,[object Object],[object Object],[object Object]

Sign and Modulus ,[object Object],[object Object],+ 28 = 0 0011100 SIGN Modulus

ACTIVITY 1 ,[object Object],[object Object],[object Object],[object Object],[object Object]

One’s Complement ,[object Object],[object Object],[object Object],-127 -75 0 75 127

One’s Complement ,[object Object],[object Object],[object Object],[object Object],[object Object]

One’s Complement ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],127 -127 65 -62 -27 100

ACTIVITY 2 ,[object Object],[object Object],[object Object]

Two’s Complement ,[object Object],[object Object]

Two’s Complement ,[object Object],[object Object],[object Object],[object Object],[object Object]

Two’s Complement ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Two’s Complement ,[object Object],[object Object],[object Object],[object Object]

ACTIVITY 3 ,[object Object],[object Object],[object Object],[object Object],[object Object]

Answers ,[object Object],[object Object],[object Object]

ANSWER ,[object Object],[object Object],[object Object],[object Object],[object Object]

Representation of Fractions ,[object Object],[object Object],[object Object],[object Object],[object Object]

Methods Used: ,[object Object],[object Object],[object Object],[object Object]

Fixed Point ,[object Object],[object Object],[object Object],[object Object],[object Object]

Fixed Point Therefore 16 + 2 + 1 = 19 (Integer) 0.5 + 0.125 = 0.625 (Fraction) So 10011.101 = 19.625 1 0 1 1 1 0 0 1 0.125 0.25 0.5 1 2 4 8 16 Fractional Integer

Fixed Point ,[object Object],[object Object]

Activity 4 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Activity 4 ,[object Object],[object Object],[object Object],[object Object]

Floating Point ,[object Object],[object Object],[object Object],[object Object]

Floating Point ,[object Object],[object Object],[object Object],[object Object],[object Object]

Activity 5 ,[object Object],[object Object],[object Object],[object Object],[object Object]

Floating Point ,[object Object],[object Object],Sign Bit Mantissa Exponent

Floating Point ,[object Object],[object Object],[object Object],1 0.0625 0 1 1 0.125 0.25 0.5

Floating Point ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

IEEE 32 Bit ,[object Object],32 Bits Sign Bit (1 bit) Exponent (8 bits) Mantissa (23 bits)

IEEE 32 Bit ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

IEEE 32 Bit ,[object Object],[object Object],[object Object],[object Object]

Activity 6 ,[object Object],[object Object]

Integer Representation

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Integer Representation