Data Representation

You will be able to

• Convert positive whole numbers between denary, binary and hexadecimal, up to 16 bits, showing the method.
• Explain why each hexadecimal digit stands for exactly four bits, and why hexadecimal is used.
• State the largest value an n-bit register can hold (2ⁿ − 1), and what happens when a result needs one more bit.

You will be able to

• Add two positive 8-bit binary integers, showing the carry in each column.
• State the four column rules of binary addition, including 1 + 1 + 1 = 11 (write 1, carry 1).
• Explain what an overflow error is and why the stored 8-bit result is then wrong.

You will be able to

• Perform a logical left or right shift of an 8-bit binary number by a given number of places.
• State the effect of a shift: left by n multiplies by 2ⁿ and right by n divides by 2ⁿ (the remainder is lost).
• Explain why a left shift gives a wrong answer once a 1 is shifted out of the most significant bit.

You will be able to

• Convert between denary and 8-bit two's complement binary, for positive and negative integers.
• Find the two's complement of a positive number by flipping every bit and adding 1, and check it with the place values.
• State the range of an 8-bit two's complement integer (−128 to +127) and explain why the most significant bit shows the sign.

You will be able to

• State the character code of a character from a given set, and use the order of the codes to deduce the code of another letter.
• Explain why Unicode is needed as well as ASCII, and why it uses more bits per character.
• Calculate the number of bits and bytes needed to store a string in a given character set.

You will be able to

• Describe how sound is sampled: the amplitude is measured at set time intervals and each sample is stored as a binary number.
• Explain how the sample rate and the sample resolution affect the accuracy of the recording and the file size.
• Calculate the file size of a sound file from its sample rate, sample resolution and length, in bits, bytes, KiB and MiB.

You will be able to

• Describe how a bitmap image is stored as pixels, each with a binary code for its colour.
• Explain how the resolution and the colour depth affect the image quality and the file size.
• Calculate the file size of a bitmap from its width, height and colour depth, in bits, bytes and KiB.

You will be able to

• Describe how run-length encoding stores each run of repeated values as a count and a value.
• Calculate the size of data before and after run-length encoding, and the saving.
• Explain why RLE is lossless and when it makes a file larger, and compare it with lossy compression.