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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1.Easy
click the bits to set them012806403201608040201

Set the bits so the 8-bit register holds 0xC6. What is the pattern's value N in decimal?

0xC6
N =
2.Easy
place values525631611

Convert the hexadecimal number 0x531 to decimal. Find N.

0x531A = 10 … F = 15
N =
3.Medium
8-bit two's complement?−128?64?32?16?8?4?2?1

Write −67 as an 8-bit two's complement pattern. Read the pattern as an unsigned binary number: what is its value U in decimal?

N = −678 bit
U =
4.Medium
8-bit two's complement?−128?64?32?16?8?4?2?1

Write −7 as an 8-bit two's complement pattern. Read the pattern as an unsigned binary number: what is its value U in decimal?

N = −78 bit
U =
5.Hard
2206 codes, b = ? bits?2ᵇ⁻¹…?4?2?1

A system must give every one of 2206 items its own binary code of the same length. What is the smallest number of bits b needed?

2206
b = bit
6.Hard
16-bit two's complement, N = ??sign???????????????

What is the most negative integer N that can be stored in 16-bit two's complement?

16 bit
N =

Answer key

  1. 1. N = 198
  2. 2. N = 1329
  3. 3. U = 189
  4. 4. U = 249
  5. 5. b = 12 bit
  6. 6. N = −32768

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