1. Convert the number 0100100100 000100 to denary
2. Represent the decimal value –57 as an 8-bit two’s complement binary integer
3. The floating point representation is used to represent integers that are very large and also for the representation of real(fractional) numbers.
4. The number 2.25 (Fixed point decimal) with an equal number of parts for the integer part and fractional part would be represented as:
5. Using eight bits in fixed-point binary the number 11.6875 would be written as:
6. Consider a really large integer - 1,234567. This number requires seven places to represent the value. If the no. of places was just four, then ________________________________
7. If more bits are assigned to the fractional part in fixed-point binary ___________________
8. Representing a large number like 1,234567 using only four places would make it: 1,234,000 and this would mean_____________
9. Read through the following rules for determining significance and answer the question. What are the significant digits?
10. So, how does all this apply to Binary? Review the modified significance rules for significance and answer the question. What are the significant bits?
11. In the binary fixed-point notation, the radix position is fixed at a certain point within the bit pattern. In the following example where four bits are used for the integer part: a7,a6,a5,a4 contain __________________
12. In the binary fixed-point notation, where four bits are used for the exponent, the a3,a2,a1 and a0 contain ____________
13. In fixed point notation, if there are four bits for the integer part and four bits for the exponent what is the range of values available?
14. The advantage of using floating-point numbers (over fixed) is that ________________
15. Floating point numbers consist of two parts:
16. In floating point binary negative numbers can be represented by:
17. In general, the mantissa is specified as a fixed-point binary number. The binary point is placed in between the _________________________________________________
18. Based on the floating point 8 bit binary byte shown in the image below, note that the a7 decides whether the number is negative or positive and is called the ________
19. The following excerpt shows the steps necessary to convert a decimal real number to floating point representation. Fill in the blanks for step 3 ………
20. One way of representing real numbers is to use the two's complement standard for both the mantissa and the exponent. In this way, a negative number could be represented by using a ___________________
21. When representing a real number using the two's complement standard for both mantissa and exponent, a number smaller than 1 could be represented by using a _____________
22. In this example, the mantissa is positive and the exponent is negative.
23. Convert the floating point 10.001 in binary into its equivalent decimal notation
24. Assuming a 16 bit register with 10 bits for the mantissa and 6 bits for the exponent, convert this into its Decimal (base 10) equivalent.
25. Assuming a 16 bit register with 10 bits for the mantissa and 6 bits for the exponent, convert this into its Decimal (base 10) equivalent..
26. Assuming a 16 bit register with 10 bits for the mantissa and 6 bits for the exponent, convert this into its Decimal (base 10) equivalent...
27. Assuming a 16 bit register with 10 bits for the mantissa and 6 bits for the exponent, convert this into its Decimal (base 10) equivalent....
28. Assuming a 16 bit register with 10 bits for the mantissa and 6 bits for the exponent, convert this into its Decimal (base 10) equivalent…..
29. If the exponent is in a format called 'excess -127', this means that the number should be worked out as a normal binary number but then 127 should be subtracted from it. 00000000 would therefore be:
30. The standard always includes ways to represent +0, -0 +infinity and -infinity. This means if a number is worked out that is larger than the storage available, it can be stored as infinity.
