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
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