b) (i)Is it possible to design a 3-bit binary code to represent each of the 7 digits of the base-7 number system that is also self-complementing? How, if it is possible, and why not, if it is not possible? (ii)Is it possible to design a 3-bit binary code to represent each of the 8 digits of the base-8 number system that is also self-complementing? How, if it is possible, and why not, if it is not possible? [Remember: a code is self-complementing when the complementary digits in base 7 encode into complementary triplets in the 3-bit representation; for instance BCD is not self-complementing, for 0 and 9 are complementing, but 0000 and 1001 are not; the 2421 code is self-complementing]

2. Determine the representation of the following decimal numbers in the floating point number system of a 32-bit word length microcomputer: (a) (7.90625) 10 and (b) (-12.875)10-

In single precision (IEEE-754 standard), 8 bits are used for storing the exponent (the bias is 127), and 23 bits are used for storing the mantissa.  (a) What are the smallest and the largest positive numbers that can be stored in single precision? (b) What is the smallest value of the mantissa that can be stored?

H - For the IEEE 754 single-precision floating point, write the hexadecimal representation for the following decimal values: (i)–1.0 (ii)– 0.0 (iii)256.015625

1. unsigned binary and decimal representations.a. Give the 16-bit unsigned binary and hexadecimal representations of thedecimal number (2040).b. Give the 16-bit unsigned binary and decimal representations of the hexnumber (B2CF).

i) The 8-bit binary (two’s-complement) conversion of the signed decimal integer -128 is what? ii) The hexadecimal representation of the binary number 1111 1101 1010 0011 0101 is?

Chapter 2: Practice Problems 1. Assume we are running code on a 8-bit machine using two's complement arithmetic for signed integers. A "short" integer is encoded using 4 bits. Fill in the empty boxes in the table below. The following definitions are used in the table: short sy = -3; int y = sy; int x = -17; unsigned ux = x Note: You need not fill in entries marked with "-" Only accepted format for binary representation (use 8-bits): 00000000, 11111111 Only accepted format for hexadecimal representation: 4D, EF, FF Expression Binary Zero ux y X >> 2 Tmax Tmax+Tmin Tmin - 1 Decimal 0 -3 00110010 Hexadecimal

(3) The IEEE 754 standard specifies a single-precision binary floating-point format (binary32) as having 1 bit for sign bit, 8 bits for exponent, and 23 bits for fractions (mantissa). Given the conversion formula as follows, value2 = (-1)'31 × (1. b22b21 . bo)2 × 2(b30b29 .b23)2-127 ... (a) encode -2.2510 ; (b) decode 0 1000 0001 011 0000 0000 0000 0000 00002

Problem 1 Considering the floating-point number format used by the IBM System/360-370 series, determine the total number of different normalized numbers that the 32-bit version of this format can represent.

11] Encode Decimal '127 7/8' into Fixed Point Binary. Express your answer in Hex. 12] Encode Decimal '-92 13/32' into IEEE 754 Floating Point. Express your answer in Hex.