Review Questions
1. What is meant by the radix or base of a number system? Briefly describe why hex representation is
used for the addresses and the contents of the memory locations in the main memory of a computer.
2. What do you understand by the l’s and 2’s complements of a binary number? What will be the
range of decimal numbers that can be represented using a 16-bit 2’s complement format?
3. Briefly describe the salient features of the IEEE-754 standard for representing floating-point
numbers.
4. Why was it considered necessary to carry out a revision of the IEEE-754 standard? What are the
main features of IEEE-754r (the notation for IEEE-754 under revision)?
5. In a number system, what decides (a) the place value or weight of a given digit and (b) the maximum
numbers representable with a given number of digits?
6. In a floating-point representation, what represents (a) the range of representable numbers and (b)
the precision with which a given number can be represented?
7. Why is there a need to have floating-point standards that can take care of decimal data and decimal
arithmetic in addition to binary data and arithmetic?
Problems
1. Do the following conversions:
(a) eight-bit 2’s complement representation of (−23)10;
(b) The decimal equivalent of (00010111)2 represented in 2’s complement form.
(a) 11101001; (b) +23
2. Two possible binary representations of (−1)10 are (10000001)2 and (11111111)2. One of them
belongs to the sign-bit magnitude format and the other to the 2’s complement format. Identify.
(10000001)2
= sign-bit magnitude and (11111111)2
= 2’s complement form
3. Represent the following in the IEEE-754 floating-point standard using the single-precision format:
(a) 32-bit binary number 11110000 11001100 10101010 00001111;
(b) (−118.625)10.
(a) 01001111 01110000 11001100 10101010;
(b) 11000010 11101101 01000000 00000000
4. Give the next three numbers in each of the following hex sequences:
(a) 4A5, 4A6, 4A7, 4A8, ;
(b) B998, B999,
(a) 4A9, 4AA, 4AB; (b) B99A, B99B, B99C
5. Show that:
(a) (13A7)16
= (5031)10;
(b) (3F2)16
= (1111110010)2.
6. Assume a radix-32 arbitrary number system with 0–9 and A–V as its basic digits. Express the mixed
binary number (110101.001)2 in this arbitrary number system.
1. What is meant by the radix or base of a number system? Briefly describe why hex representation is
used for the addresses and the contents of the memory locations in the main memory of a computer.
2. What do you understand by the l’s and 2’s complements of a binary number? What will be the
range of decimal numbers that can be represented using a 16-bit 2’s complement format?
3. Briefly describe the salient features of the IEEE-754 standard for representing floating-point
numbers.
4. Why was it considered necessary to carry out a revision of the IEEE-754 standard? What are the
main features of IEEE-754r (the notation for IEEE-754 under revision)?
5. In a number system, what decides (a) the place value or weight of a given digit and (b) the maximum
numbers representable with a given number of digits?
6. In a floating-point representation, what represents (a) the range of representable numbers and (b)
the precision with which a given number can be represented?
7. Why is there a need to have floating-point standards that can take care of decimal data and decimal
arithmetic in addition to binary data and arithmetic?
Problems
1. Do the following conversions:
(a) eight-bit 2’s complement representation of (−23)10;
(b) The decimal equivalent of (00010111)2 represented in 2’s complement form.
(a) 11101001; (b) +23
2. Two possible binary representations of (−1)10 are (10000001)2 and (11111111)2. One of them
belongs to the sign-bit magnitude format and the other to the 2’s complement format. Identify.
(10000001)2
= sign-bit magnitude and (11111111)2
= 2’s complement form
3. Represent the following in the IEEE-754 floating-point standard using the single-precision format:
(a) 32-bit binary number 11110000 11001100 10101010 00001111;
(b) (−118.625)10.
(a) 01001111 01110000 11001100 10101010;
(b) 11000010 11101101 01000000 00000000
4. Give the next three numbers in each of the following hex sequences:
(a) 4A5, 4A6, 4A7, 4A8, ;
(b) B998, B999,
(a) 4A9, 4AA, 4AB; (b) B99A, B99B, B99C
5. Show that:
(a) (13A7)16
= (5031)10;
(b) (3F2)16
= (1111110010)2.
6. Assume a radix-32 arbitrary number system with 0–9 and A–V as its basic digits. Express the mixed
binary number (110101.001)2 in this arbitrary number system.
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