Represent the following real numbers as 16-bit FP numbers with 4-bit biased expo

Question

Represent the following real numbers as 16-bit FP numbers with 4-bit biased exponent bias = 8 and 11 - bit fractions:

a. 1.0

b. 0.5

c. 0.25

Explanation / Answer

a. 1.0 1.0 in binary is 1.0 => 1.0 * 2^0 sign bit is 0(+ve) exp bits are (7+0 = 7) => in binary it is 0111 frac bits are 00000000000 1.0 in 16-bit FP format is 0 0111 00000000000 b. 0.5 0.5 in binary is 0.1 => 1.0 * 2^-1 sign bit is 0(+ve) exp bits are (7-1 = 6) => in binary it is 0110 frac bits are 00000000000 0.5 in 16-bit FP format is 0 0110 00000000000 c. 0.25 0.25 in binary is 0.01 => 1.0 * 2^-2 sign bit is 0(+ve) exp bits are (7-2 = 5) => in binary it is 0101 frac bits are 00000000000 0.25 in 16-bit FP format is 0 0101 00000000000

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