Convert from 32-bit IEEE 754 Floating Point Standard (in hexadecimal) to decimal: 410C0000, with the following layout: first bit is sign bit, next 8 bits is exponent field, and remaining 23 bits is mantissa field; result is to be rounded up if needed.
answer choices
9.125
8.75
7.75
4.625
6.3125
Answer: ---------- b) 8.75 Explanation: ------------- Hexadecimal Binary 0 0000 1 0001 2 0010 3 0011 4 0100 5 0101 6 0110 7 0111 8 1000 9 1001 A 1010 B 1011 C 1100 D 1101 E 1110 F 1111 Use this table to convert from hexadecimal to binary Converting 410C0000 to binary 4 => 0100 1 => 0001 0 => 0000 C => 1100 0 => 0000 0 => 0000 0 => 0000 0 => 0000 So, in binary 410C0000 is 01000001000011000000000000000000 0 10000010 00011000000000000000000 sign bit is 0(+ve) exp bits are 10000010 => 10000010 => 1x2^7+0x2^6+0x2^5+0x2^4+0x2^3+0x2^2+1x2^1+0x2^0 => 1x128+0x64+0x32+0x16+0x8+0x4+1x2+0x1 => 128+0+0+0+0+0+2+0 => 130 in decimal it is 130 so, exponent/bias is 130-127 = 3 frac bits are 00011 IEEE-754 Decimal value is 1.frac * 2^exponent IEEE-754 Decimal value is 1.00011 * 2^3 1.00011 in decimal is 1.09375 => 1.00011 => 1x2^0+0x2^-1+0x2^-2+0x2^-3+1x2^-4+1x2^-5 => 1x1+0x0.5+0x0.25+0x0.125+1x0.0625+1x0.03125 => 1+0.0+0.0+0.0+0.0625+0.03125 => 1.09375 so, 1.09375 * 2^3 in decimal is 8.75 so, 01000001000011000000000000000000 in IEEE-754 single precision format is 8.75 Answer: 8.75
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