Number systems worksheet with answers

Free printable Number systems worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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Name: ____________________   Date: ____________

1.Easy
place values112816413201608040201

Convert the binary number 1110 0000₂ to decimal. Find N.

1110 0000₂
N =
2.Easy
place valuesC25601681

Convert the hexadecimal number 0xC08 to decimal. Find N.

0xC08A = 10 … F = 15
N =
3.Medium
place values in two's complement1−12806413201608140201

The 8-bit pattern 1010 0100 stores a signed integer in two's complement. What is its value N in decimal?

1010 01008 bit
N =
4.Medium
8-bit two's complement?−128?64?32?16?8?4?2?1

Write −31 as an 8-bit two's complement pattern. Read the pattern as an unsigned binary number: what is its value U in decimal?

N = −318 bit
U =
5.Hard
4817 codes, b = ? bits?2ᵇ⁻¹…?4?2?1

A system must give every one of 4817 items its own binary code of the same length. What is the smallest number of bits b needed?

4817
b = bit
6.Hard
24 bit1 px640 px480 pxM = ? KiB

An uncompressed image is 640 × 480 pixels with 24 bits per pixel. How much memory M does it take, in KiB (1 KiB = 1024 bytes)?

640 × 480 px24 bit/px1 KiB = 1024 B
M = KiB

Answer key

  1. 1. N = 224
  2. 2. N = 3080
  3. 3. N = −92
  4. 4. U = 225
  5. 5. b = 13 bit
  6. 6. M = 900 KiB

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