Number representation (Floating Point)

Convert 0010 1100₂ to hexadecimal

• 2C

• 2B

• 44

• 2D

Convert 3D₁₆ to 8 bit binary

• 1111010

• 00111001

• 00111101

• 00111011

Convert 0010 1100₂ to denary

• 42

• 44

• 34

• 46

Convert -20 to 8 bit twos compliment

• 1001 0100

• 1110 1011

• 1110 1100

• 1110 1000

In 2.4 x 10^-3 which number is the mantissa?

• 2.4

• 10

• -3

• x

In 2.4 x 10^-3 which number is the exponent?

• 2.4

• 10

• -3

• x

Convert 3.25 to floating point, 8 bit mantissa, 4 bit exponent

• M=0110 1000 E=0010

• M=0011 1000 E=0011

• M=1000 1100 E=0100

• M=0111 0100 E=0011

Answer explanation

Convert 3.25 to floating point

3.25 = 11.01

Positive so just need to normalise

M = 0.110 1000

Moved the point 2 places left so

E = 0010

Convert -34.5 to floating point, 8 bit mantissa, 4 bit exponent

• M=10111010 E=0110

• M=10110011 E=0110

• M=10111011 E=0110

• M=11101100 E=0111

Answer explanation

Convert -34.5 to floating point

+34.5 = 0100010.1 (leading 0 needed as positive)

Flip the bits and add one (negative)

1011101.1

Normalise - shift the decimal point left 6 times

M = 1.0111011 (we can leave out the . as it is implied)

E = 0110

Convert 20 to floating point, 8 bit mantissa, 4 bit exponent

• M=0010 1000 E=0110

• M=0101 0000 E=0101

• M=0001 0100 E=0000

• M=0100 1000 E=0101

Answer explanation

Convert 20 to floating point

20 = 010100.00

Positive so just normalise

M = 0.1010000

Point moved 5 to the left so

E = 0101

Convert -0.25 to floating point, 8 bit mantissa, 4 bit exponent

• M=0100 0000 E=0000

• M=10000000 E=1110

• M=1111 1111 E=1110

• M=1010 0000 E=1111

Answer explanation

Convert -0.25 to floating point, 8 bit mantissa, 4 bit exponent

+0.25 is 0.0100000 in binary

-0.25 is 1.1100000 (flip the bits and add one)

Normalise (move the point so it starts 1.0)

1.0000000

Moved the point right twice so exponent = -2

Twos compliment = 1110