Podcast
Questions and Answers
What is the result of 100111 / 11?
What is the result of 100111 / 11?
1101
Find the representation error for -0.35 using 4-bits two's complement.
Find the representation error for -0.35 using 4-bits two's complement.
0.05
What is the resolution of the code in Method 2 when it is 0.3 and M is 2?
What is the resolution of the code in Method 2 when it is 0.3 and M is 2?
0.15
Find the representation error for -0.25 in fixed point fractional using 5-bits fractional two's complement.
Find the representation error for -0.25 in fixed point fractional using 5-bits fractional two's complement.
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Which method uses at least 13 levels and requires 4 bits?
Which method uses at least 13 levels and requires 4 bits?
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What is the dynamic range for the floating-point code designed with a range of [-15, 20]?
What is the dynamic range for the floating-point code designed with a range of [-15, 20]?
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Represent 0.210 in the floating-point code design.
Represent 0.210 in the floating-point code design.
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Calculate the representation error for 0.210 in the floating-point code design.
Calculate the representation error for 0.210 in the floating-point code design.
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Study Notes
Tutorial 1: Number Systems
- The lecturer is Dr. (Alex) Yu Gong.
- The tutorial covers number systems, including binary, decimal, and hexadecimal representations.
Binary Division
- The tutorial starts with an example of binary division: 10010111 ÷ 11.
- The solution is shown step-by-step, with the dividend, divisor, and quotient.
Tutorial 2: Two's Complement Codes
- The tutorial covers three methods to apply two's complement codes.
- Method 1: Normalize to an integer range.
- Dynamic range: [-2.4, 1.5]
- Resolution: 0.3
- Normalize to [-8, 5]
- 4-bit two's complement code: 1101
- Representation error: 0.05
- Method 2: Fixed-point fractional representation.
- Resolution: 0.3, choose M = 2
- Dynamic range: [-2^3, 2^3 - 1] = [-8, 7]
- 5-bit two's complement code: 11101
- Representation error: 0.1
- Method 3: Direct match.
- Dynamic range: [-2.4, 1.5]
- Resolution: 0.3
- At least 13 levels are needed, which require 4 bits.
- Quantize the values into 16 levels.
- Representation error: 0.014
Representation of -0.35
- Method 1: Normalize to an integer range.
- Representation: 1101
- Representation error: 0.05
- Method 2: Fixed-point fractional representation.
- Representation: 11101
- Representation error: 0.1
- Method 3: Direct match.
- Representation: 1001
- Representation error: 0.014
Comparison of the Three Methods
- The three methods are compared in terms of dynamic range, resolution, and overhead.
- The results are shown in a table.
Tutorial 3: Floating-Point Codes
- The tutorial covers the design of floating-point codes.
- The requirements are:
- Dynamic range: [-15, 20]
- Relative resolution: 10%
- The design involves:
- Sign bit: 1 bit
- Exponent: 3 bits
- Fractional part: 4 bits
- Implied bit: 0
- Exponent bias: 2
Representation of Numbers
- The representation of several numbers is shown:
- 0.2
- -0.11
- 0.0051
- -3.11
- The representation error is calculated for each number.
Floating-Point Representation
- The floating-point representation is shown:
- Sign bit: 1 bit
- Exponent: 3 bits
- Fractional part: 4 bits
- Implied bit: 0
- Exponent bias: 2
- The value of the representation is calculated:
- (−1)^S × 2^(E-2) × (1 + F)
- The representation of the smallest and largest positive subnormal numbers is shown.
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Description
Solve division problems in number systems, including binary division. Practice exercises and solutions provided by Dr. Alex Yu Gong.