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1) Represent the following decimal numbers using IEEE-754 Floating point represe

ID: 3599540 • Letter: 1

Question

1) Represent the following decimal numbers using IEEE-754 Floating point representation (a) 0.5 (b) -0.75 (c) 0 2) Using the knowledge of NMOS and PMOS transistors we learned in class, propose how you would design the following gates in CMOS: (NOTE: It is inefficient to use two separate 2-input gates to implement this) a) A 3-input NAND gate b) A 3-input NOR gate c) Propose a general rule for designing n-input gates. How many transistors would be required for an n-input NAND gate or n-input NOR gate? d) How many transistors are needed to construct the following: (No drawing is necessary) (i) 4-input AND gate (i) 7-input OR gate_

Explanation / Answer

1

a)Decimal Value = 0.5

Single precision (32 bits):

Binary:    

Status: normal

Bit 31

Sign Bit = 0

0: +

1: -

Bits 30 - 23

Exponent Field = 01111110

Decimal value of exponent field and exponent

126 - 127 = -1

Bits 22 - 0

Significand = 1 .00000000000000000000000

Decimal value of the significand

1.0000000

Hexadecimal: 3F000000

   Decimal: 5.0000000e-1

b)Decimal Value : -0.75

Single precision (32 bits):

Binary:    

Status: normal

Bit 31

Sign Bit=1

0: +

1: -

Bits 30 - 23

Exponent Field=01111110

Decimal value of exponent field and exponent

126 - 127 = -1

Bits 22 - 0

Significand=1 .10000000000000000000000

Decimal value of the significand=1.5000000

Hexadecimal: BF400000

   Decimal: -7.5000000e-1

c) Decimal Value: 0

Single precision (32 bits):

Binary:    

Status: normal

Bit 31

Sign Bit=0

0: +

1: -

Bits 30 - 23

Exponent Field=00000000

Decimal value of exponent field and exponent

0 - 127 = -127

Bits 22 - 0

Significand= 0.0000000000000000000000

Decimal value of the significand=0.0000000

Hexadecimal: 00000000

   Decimal: 0.0000000

d) infinity is a Nan value so the floating point is 0 as above