EEE3002 Microprocessors Tutorial 1 (2014 Semester 1) 1) Find the two’s complement representation for the following numbers, assuming that they are represented as a 16-bit number. Write the value in both binary and hexadecimal. a) −93 b) 1034 c) 492 d) −1094

1) Using the smallest data size possible, either a byte, a halfword (16 bits), or a word (32 bits), convert the following values into two’s complement representations: e) −18,304 f) −20 g) 114 h) −128

2) Convert the following hexadecimal values to base ten: i) 0xFE98 j) 0xFEED k) 0xB00 l) 0xDEAF

3) Convert the following decimal numbers into hexadecimal m) 256 n) 1000 o) 4095 p) 42

4) Convert the following fractions into decimal numbers q) Binary number : 101.111 r) Hexadecimal number : 101.111

5) Convert the following numbers into binary numbers s) Decimal number: 8.625 t) Hexadecimal number : A1.E8

6) List the advantages of using the two’s complement representation over the more intuitive sign-magnitude representation.

EE3002 Microprocessors Tutorial 1 Solutions (2014 Semester 2)

1) Steps * First convert the magnitude number into binary. * If number is positive, stop, else proceed to next step. * Compute the 1’s complement by inverting the bits. * Add 1 to the 1’s complement to obtain the 2’s complement number.

a) 93 = 1 0 1 1 1 0 1 B
Can be converted by hand using repeated division by 2 and keeping track of the remainders.

2∟93
2∟46 Remainder 1 (Least Significant bit)
2∟23 Remainder 0
2∟11 Remainder 1
2∟5 Remainder 1
2∟2 Remainder 1
2∟1 Remainder 0 0 Remainder 1

In 16-bit format, 93 can be represented as

0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 B

Invert the bits to get