Data Representations

Topics covered: Base conversions, Binary, Hexadecimal, Binary Addition/multiplication, 2’s Complement, Extended Precision, Floating Point encodings

What is the binary representation of 73?

Convert 111010102 to base 10.

Add 5210 and 3410 as unsigned integers in binary, show the result in binary.

Multiply 510 and 2410 as unsigned integers in binary, show the result in binary.

What is the hex code for an integer which contains alternating 1’s and 0’s, starting with a 1?

What is the hex code for an integer where the most significant byte is all 1’s, the next is all 1’s, and next is all 0’s, and the last is all 1’s?

What is the hex code for the most positive int value in C/C++?

What is the hex code for the most negative int value in C/C++?

What is the 2’s complement representation of 70 using 8 bits?

What is the 2’s complement representation of -34 using 8 bits?

Add 28 and -9 using 2’s complement using 8 bits.

Add -52 and -4 using 2’s complement using 8 bits.

Perform 55 – 89 using 2’s complement using 8 bits.

If you had the C code int a = 68, what shifting operation could be done to multiply a by 64 without using multiplication?

If you had the C code int a = 68, and you did a = a>>1 fifty times, what would be the value of a? Explain why.

If you had the C code int a = 68, and you did a = a<<1 fifty times, what would be the value of a? Explain why.

If you had the C code int a = -68, and you did a = a>>1 thirty three times, what would be the value of a? Explain why.

1 . answer : Binary 73 = 10010012
The binary for 73 is 1001001

• Type pi for =3.14159…, e for e=2.71828…, sqrt(2 for 2√2 = 1.41421…
• Please use capital letters in the representations of base >10.
• The algebraic operations + – * / ^ are allowed, as well as pairs of parentheses. Accepted transcendental functions are sin(), cos(), exp(), log(), atan().

3. answer: Binary 8620 = 100001101011002
The binary for 8620 is 10000110101100

4. 1011100011

5. answer is : integers must be start from 0 or 1

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