Practice Problems

1-What is the value of the 8-bit binary quantity 10101000 if it is interpreted

a-as an unsigned integer and

b-as a signed integer represented in sign/magnitude notation?

2-What does the unsigned decimal value 99 look like in binary using 8 bits?

3-What do the signed integers 300 and +254 look like in binary using 10 bits and sign/magnitude integer representation?

4-What is the value of the 8-bit binary quantity 10010111 when it is interpreted as a sign/magnitude integer?

5-Using 4 bits and twos complement representation, what is the binary representation of the following signed decimal values:

a) +6

b) 3

6) Perform the following 5-bit binary addition showing the carry bit that propagates to each column. Assume that the numbers are unsigned binary quantities:

01110

+ 01011

7-What does the three-character string X+Y look like internally using the 8-bit ASCII code given in table below? What does it look like in 16-bit Unicode? (Go to www.unicode.org to find the specific code mappings for these three characters.)

1. 8-Using 10 bits to represent the mantissa (sign/magnitude) and 6 bits for the exponent (also sign/magnitude), show the internal representation of the following two values:

   1. +0.25

   2. 32 1/16

2. 9-Explain exactly what happens when you add a 1 to the following 5-bit, twos complement value: 01111

3. 10-Explain exactly what happens when you perform addition on the following two sign/magnitude integer values:

   00111 (+7)

   +01110 (+14)