Excess-N and Biased Number Representations Essentials Quiz Quiz

Explore the basics of excess-N and biased number representations with this easy quiz designed to reinforce understanding of digital encoding systems, binary representations, and key conversion concepts in computer architecture.

1. Understanding Excess-N Notation

   In excess-3 encoding, what is the excess value that gets added to the actual number before encoding in binary format?

   1. 3
   2. 2
   3. 4
   4. 8

   Explanation: In excess-3 representation, the number 3 is added to the original decimal digit before encoding it in binary. Options 2, 4, and 8 are incorrect because they refer to different excess/bias values or do not relate to excess-3 specifically.

2. Purpose of Biased Representation

   Why do digital systems use biased number representations such as excess-127 for exponents in floating-point numbers?

   1. To save memory space
   2. To avoid using zeros
   3. To represent signed numbers with unsigned binary values
   4. To increase processing speed arbitrarily

   Explanation: Biased representations like excess-127 help represent both positive and negative numbers using only non-negative (unsigned) binary values. Saving memory space and increasing processing speed are not direct reasons for using biased representations. Avoiding zeros is not the goal, as zeros can still be represented.

3. Converting Decimal to Excess-N

   If the decimal number 8 is to be represented in excess-5 coding, what value is stored in binary?

   1. 1101
   2. 0110
   3. 1001
   4. 1110

   Explanation: Excess-5 means you add 5 to the decimal number, so 8 + 5 = 13. The binary form of 13 is 1101. 1001 is the binary for 9, 1110 for 14, and 0110 for 6, none of which represent the correct excess-5 encoding for 8.

4. Identifying the Bias Value

   Given an encoding labeled 'excess-7,' what is the bias added to the original number during conversion?

   1. 17
   2. 14
   3. 70
   4. 7

   Explanation: Excess-7 notation indicates that 7 is the value added to each original number. 17, 14, and 70 are unrelated numbers and do not correspond to the bias in excess-7 representation.

5. Choosing the Correct Binary Representation

   What is the excess-4 binary representation for the decimal value 2?

   1. 0110
   2. 0010
   3. 0111
   4. 0100

   Explanation: You add 4 to the decimal value: 2 + 4 = 6, which is 0110 in binary. 0100 is binary for 4, 0010 for 2, and 0111 for 7; none of these match the excess-4 encoding for 2.

6. Understanding Biased Representation Range

   If you use excess-127 (bias 127) with an 8-bit binary field, what is the encoded binary value for the decimal zero?

   1. 01111111
   2. 00000001
   3. 11111111
   4. 00000000

   Explanation: To represent zero, add the bias: 0 + 127 = 127. In binary, 127 is 01111111 with 8 bits. 00000001 is 1, 00000000 is 0, and 11111111 is 255, none of which are the correct excess-127 representation for zero.

7. Reversing an Excess-N Conversion

   If a stored value in excess-4 representation is 1001 (binary), what is the original decimal value?

   1. 5
   2. 12
   3. 13
   4. 9

   Explanation: 1001 in binary is 9; subtract the bias 4 to find 9 - 4 = 5. Options 13 and 12 are much larger than 9, and 9 assumes no bias subtraction, which isn't correct.

8. Bias in Excess-N vs. Two’s Complement

   How does biased notation (like excess-N) differ from two’s complement in representing negative values?

   1. Both use the same method for negative numbers
   2. Two’s complement uses excess-3 encoding
   3. Biased notation multiplies the number by the bias
   4. Biased notation uses an offset, unlike two’s complement which flips bits and adds one

   Explanation: Biased notation offsets the stored values, representing negatives through subtraction of the bias. Two’s complement represents negatives by inverting bits and adding one. Biased notation does not multiply, and two’s complement does not use excess-3 encoding. The two systems use different methods.

9. Excess-N Representation Scenario

   If a digital display uses excess-3 encoding, what would be the encoded binary for displaying the digit 6?

   1. 1001
   2. 1100
   3. 0110
   4. 1010

   Explanation: 6 in excess-3 is 6 + 3 = 9, which is 1001 in binary. 0110 is 6 in straight binary, 1100 is 12, and 1010 is 10—none are the correct excess-3 binary code for 6.

10. Definition of Excess-N Representation

    Which statement best describes excess-N (biased) number representation?

    1. It encodes decimal numbers using ten binary digits
    2. It is only used for negative numbers
    3. It randomly assigns values to binary patterns
    4. It is a binary encoding where each value is shifted by a fixed bias

    Explanation: Excess-N or biased notation shifts each encoded value by a certain fixed bias. It doesn’t use ten binary digits as in option two, doesn’t assign binary patterns randomly, and is not exclusive to negative numbers.