Worksheet on Numbers

Last Three Problems

14. 95₁₀ as a BCD number

write 9 and 5 in binary

Answer: 1001 0101

15. 1 | 011111001 | 0110110000000 is the bit pattern

the leading one indicates negative, negative numbers are stored as the 2's complement of the entire positive representation, so to get the answer must take the 2's complement to work on the positive value

- 0 | 100000110 | 10010100000000

exponent portion = 100000110 =256+4+2

subtract off the value plus amount, answer is 6

now have -.100101 x 2⁶

eliminate the base and exponent by moving the radix point, to the right since positive, making a large number.

Answer: - 100101.

16. Working the opposite direction

.00001101 = + .1101 x 2^-4

exponent is -4 +256 = 252 = 011111100

expand mantissa to required number of bits

Answer: 0 | 011111100 | 11010000000000