Question Set on Algebra

1. What is the exact number of bits in a memory that contains 640M bits?

640 · 1024 = 655,360 · 1024 = 671,088,640 bits.

2. How many bits are in 1 Tb? You are asked to figure out the exact result. Hint: Depending on the tool used to calculate this, you may need to use a trick to get the exact result. Note that 220 = 1,000,00010 + d, where d is the difference between 220 and 1,000,00010, and that 1T = (1,000,00010 + d)2

8 bits/byte => 8 · 1 trillion or 812 => 8,000,000,000,000

3. Convert the binary number 1010110.1001 to decimal.

64 32 16 8 4 2 1 .5 .25 .125 .0625 1 + 0 + 1 + 0 + 1 + 1 + 0. 1 + 0 + 0 + 1

64 + 16 + 4 + 2 + .5 + .0625 = 86.5625

4. Convert the decimal number 1938.257 to hexadecimal.

1938 914 402 156 18 2
-1024 -512 -256 -128 64 32 -16 8 4 -2 1. 914 402 156 18 2 0 1 1 1 1 0 0 1 0 0 1 0 Binary 7 9 2 Hexadecimal (before radix)

Binary Hexadecimal (after radix)
.257 · 2 = .514 0 4
.514 · 2 = .028 1
.028 · 2 = .056 0
.056 · 2 = .112 0

.112 · 2 = .224 0 1
.224 · 2 = .448 0
.448 · 2 = .869 0
.869 · 2 = .792 1

.792 · 2 = .584 1 C
.584 · 2 = .168 1
.168 · 2 = .336 0
.336 · 2 = .672 0

.672 · 2 = .344 1 A
.334 · 2 = .688 0
.688 · 2 = .376 1
.376 · 2 = .752 0

.752 · 2 = .504 1 C
.504 · 2 = .008 1
.008 · 2 = .016 0
.016 · 2 = .032 0

.032 · 2 = .064 0 0
.064 · 2 = .128 0
.128 · 2 = .256 0
.256 · 2 = .512 0

.512 · 2 = .024 1 8
.024 · 2 = .048 0
.048 · 2 = .096 0
.096 · 2 = .192 0

.192 · 2 = .384 0 3
.384 · 2 = .768 0
.768 · 2 = .536 1
.536 · 2 = .072 1

.072 · 2 = .144 0 1
.144 · 2 = .288 0
.288 · 2 = .576 0
.576 · 2 = .152 1

.152 · 2 = .304 0 2
.304 · 2 = .608 0
.608 · 2 = .216 1
.216 · 2 = .432 0

Final Hexadecimal answer: 792.41CAC08312

5. Perform the binary multiplication 100111 x 011011.

100111 x