In: Computer Science
Using 64-bit IEEE 754 DOUBLE precision floating point with one(1) sign bit, eleven (11) exponent bits and fifty-two (52) mantissa bits, what is the decimal value of: 0xBFE4000000000000
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 BFE4000000000000 to binary B => 1011 F => 1111 E => 1110 4 => 0100 0 => 0000 0 => 0000 0 => 0000 0 => 0000 0 => 0000 0 => 0000 0 => 0000 0 => 0000 0 => 0000 0 => 0000 0 => 0000 0 => 0000 So, in binary BFE4000000000000 is 1011111111100100000000000000000000000000000000000000000000000000 1011111111100100000000000000000000000000000000000000000000000000 1 01111111110 0100000000000000000000000000000000000000000000000000 sign bit is 1(-ve) exp bits are 01111111110 => 01111111110 => 0x2^10+1x2^9+1x2^8+1x2^7+1x2^6+1x2^5+1x2^4+1x2^3+1x2^2+1x2^1+0x2^0 => 0x1024+1x512+1x256+1x128+1x64+1x32+1x16+1x8+1x4+1x2+0x1 => 0+512+256+128+64+32+16+8+4+2+0 => 1022 in decimal it is 1022 so, exponent/bias is 1022-1023 = -1 frac bits are 01 IEEE-754 Decimal value is 1.frac * 2^exponent IEEE-754 Decimal value is 1.01 * 2^-1 1.01 in decimal is 1.25 => 1.01 => 1x2^0+0x2^-1+1x2^-2 => 1x1+0x0.5+1x0.25 => 1+0.0+0.25 => 1.25 so, 1.25 * 2^-1 in decimal is 0.625 so, 0xBFE4000000000000 in IEEE-754 double precision format is -0.625 Answer: -0.625