Number System Questions

1)In a microcomputer, the addresses of memory locations are binary numbers that identify each memory circuit where a byte is stored. The number of bits that make up an address depends on how many memory locations there are. Since the number of bits can be very large, the addresses are often specified in hex instead of binary.

(a) If a microcomputer uses a 20-bit address, how many different memory locations are there?
(b) How many hex digits are needed to represent the address of a memory location?
(c) What is the hex address of the 256th memory location? (Note: The first addres is always 0.)

2) In an audio CD, the audio voltage signal is typically sampled about 44,000 times per second, and the value of each sample is recorded on the CD surface as a binary number. In other words, each recorded binary number represents a single voltage point on the audio signal waveform.

(a) If the binary numbers are six bits in length, how many different voltage values can be represented by a single binary number?
Repeat for eight bits and ten bits.

(b) If ten-bit numbers are used, how many bits will be recorded on the CD in 1 second?
(c) If a CD can typically store 5 billion bits, how many seconds of audio can be recorded when ten-bit numbers are used?

Sample Solution