1.7 Add the following numbers in binary using 2's complement to represent negative numbers.  Use a word length of 6 bits (including sign) and indicate if an overflow occurs.  (a) 21 + 11  (d) (−12) + 13  (e) (−11) + (−21)

1.9 Suppose we use six bits to represent a two's complement binary number. (a) What is the largest number that can be represented? (b) What is the smallest number that can be represented? (c) How many total base-10 numbers can be represented?

Description Find the sum of 10.2510 and 5.2510 using the 14-bit "simple" floating-point model. Hint: Refer to slides or class notes for a similar example.

3.26 Let A be an 8-bit input. Fill in the table showing the promotion to 16-bit unsigned and ie bit signed. Give all answers in 16-bit hexadecimal. The first row illustrates the process. Unsigned 16-bit Signed 16-bit 0x80 0x51 0x0080 OXFF80 OXED Ox00 OXBF

Example: Assuming m-7 bits and using three of those bits for representing the fractional part, ( 1100.000 )2 ( 0110.000 )2 ( 0011.000 )2 ( 0001.100 )2 ( 0000.110 )2 ( 0000.011 )2 (12)10 %3D (12)10 / 2 (6)10 (6)10 /2 (3)10 (3)10 /2 (1.5)10 (1.5)10 / 2 (0.75)10 (0.75)10 / 2 (0.375)10 In this case, each successive division by two has shifted the binary sequence to the right by one bit.

1) Convert the following decimal numbers to the 9’s complement: Perform subtraction using 9’s complement on 26-18   2)Convert the following decimal numbers to the 10’s complement: Perform subtraction using 10’s complement on 432-567   3) Perform the following multiplications. Assume that all values are unsignednumbers. (No problem with unsigned (always positive) numbers, just use the samestandard techniques as in base 10.) a. 1010 * 0110

1) Convert the following decimal numbers to the 9’s complement: Perform subtraction using 9’s complement on 26-18   2)Convert the following decimal numbers to the 10’s complement: Perform subtraction using 10’s complement on 432-567   3) Perform the following multiplications. Assume that all values are unsignednumbers. (No problem with unsigned (always positive) numbers, just use the samestandard techniques as in base 10.) a. 1010 * 0110

ES) Convert 27.3410 to octal. If the answer is irrational, stop at four digits after number point. (us) Convert 0.110 to binary. Can you accurately represent the same value in binary using a certain number of bits? Why or why not? What is the relationship between the three numbers below? Explain why it is the case. xyzb xyzob xy.zb Here x, y, and z are all valid single-digit values in the number system in base b and b is an integer larger than 1.

6. Using only the binary shift left operation, how can one multiply a number by decimal 16?

Perform the following tasks by explaining the process of each one in detail: 1. Converting all numbers by follow between brackets: a. 487.2 from base 10 to [ bases 2,8, 16] b. 11010110 from base 2 to [ base 10 ] c. 456 from base 8 to [ base 10 ] d. 2B6 from base 16 to [ base 10 ] 2. Adding all numbers by follow between brackets: a. The binary numbers: [11010110 + 10000101] b. The octal numbers: [ 456 + 555 ] c. The hexadecimal numbers: [ 2B6 + 12C] 3. Subtracting all numbers by follow between brackets: a. The binary numbers: [ 11010110 - 10000101] b. The octal numbers: [ 555 – 456 ] c. The hexadecimal numbers: [ 2B6 - 12C]