16. Convert the following decimal values to binary. Indicate which can or cannot be stored precisely as floats. (a) 5.125 (b) 14.6 (c) 8.5 (d) 3.65625
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- 16. Convert the following decimal values to binary. Indicate which can or cannot be stored precisely as floats. (a) 5.125 (b) 14.6 (c) 8.5 (d) 3.65625Use the appropriate conversion of floating point binary numbers torepresent the following binary numbers as decimal numbers.i) 1011.11 ii) 101101.101 iii) 1.101101 x 24 iv) 1.011 x 2-1and s) At least how many bits are needed to represent the decimal number 3,175,000 in binary? How many bytes will it take to store this number? Note that 1 byte includes 8 bits.
- 21. Express the decimal numbers that follow as (a) 29 (b) 88 unpacked and packed BCD bytes. esp9. Show how the text ‘HelloW’ will be stored in computer using 7-bit ASCII standard. You will need to consult the ASCII table. 10. Fill in the following addition table for base 3.1-6 Convert the following decimal numbers to the indicated bases: (a) 7562.45 to octal. (b) 1938.257 to hexadecimal. (c) 175.175 to binary. 1-7 Convert the hexadecimal number F3A7C2 to binary and octal. 1-8 Convert the following numbers from the given base to the other three bases indicated. (a) Decimal 225 to binary, octal, and hexadecimal. (b) Binary 11010111 to decimal, octal, and hexadecimal. (c) Octal 623 to decimal, binary, and hexadecimal. (d) Hexadecimal 2AC5 to decimal, octal, and binary.
- 1) IEEE 754 Floating Point Standard: This standard is used to represent floating-point numbers (real numbers) digitally in computer memory. The standard provides two representations which have different accuracies: double precision and single precision. > Double Precision – 8bytes = 64 bits o Bit 63 (one bit): Sign (0=positive, 1=negative) o Bits 62 to 52 (11 bits): Exponent, biased by 1023 o Bits 51 to 0 (52 bits): Fraction f of the number 1.f Single Precision – 4bytes = 32 bits o Bit 31 (one bit): Sign (0-positive, 1=negative) o Bits 30 to 23 (8 bits): Exponent, biased by 127 o Bits 22 to 0 (23 bits): Fraction f of the number 1.f Procedure to Find the Double-Precision Representation of a Number x: Let the representation be (b63, b62, ..., b, b,, bo) with b63 being the most-significant bit and bo being the least significant bit. Sign Bit: (0, x20 l1, x1 { set new bit as 1 y + y-1 else set new bit as 0 EE 426 Homework 2 Spring 2020/2021 a) Find the double-precision representation of…Q1. (a) (8%) Convert and elaborate the following decimal numbers into binary, and then binary into hexadecimal equivalents:(i) 12010 (ii) 20010 (b) (8%) Convert the following decimal numbers into hexadecimal equivalents by hex- dabble method: (i) 455010 (ii) 204010 (c) (4%) Write the machine code in binary as well as its hexadecimal equivalent for the instruction "MVI A, F3,".6. Convert the following numbers from unsigned binary notation to decimal notation, and from 6-bit 2's complement notation to decimal notation: i) 110011, ii) 001101, iii) 101101 7. Show how each of the following floating point values would be stored using IEEE-754 single precision (be sure to indicate the sign bit, the exponent, and the significand fields): a. 12.5 b. −1.5 c. 0.75 d. 26.625 8. The following is a representation of a decimal floating value using IEEE-754 single precision. Find out the value in decimal. 0 10000011 10101000000...0
- 7. Fill in the memory map with the hexadecimal byte values that are defined by the following. The first byte is given. ASCII table is given on last page. db 25, 50, 75, XYZ' dw 500, 1000, -1500 numbers list numbers 1911. Convert each of the following numbers to base of 10:(a) (34A)16(b) (FAC)169)The following numbers use the IEEE 32-bit floating-point format. What is the equivalent decimal value? (a) 1 10000011 11000000000000000000000 (b) 0 01111110 10100000000000000000000 (c) 0 10000000 00000000000000000000000